One cyclist travels at x mi/h, the other at x-2 mi/h. Their rates are 41 mi/h and 39 mi/h.
Let's call the rate of the faster cyclist "x" and the rate of the slower cyclist "x-2" (since we know the slower cyclist travels at 2 mi/h slower).
We know that they are traveling in opposite directions, so we can add their rates together to find the total distance traveled: x + (x-2) = 2x - 2.
We also know that after 3 hours, they are 123 miles apart, so we can set up the equation: 3(x + x-2) = 123.
Simplifying this equation gives us: 6x - 6 = 123, which we can solve for x: 6x = 129, x = 21.5.
So the faster cyclist is traveling at a rate of 21.5 mi/h, and the slower cyclist is traveling at a rate of 19.5 mi/h.
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One cyclist travels at x mi/h, the other at x-2 mi/h. Their rates are 41 mi/h and 39 mi/h.
Let's call the rate of the faster cyclist "x" and the rate of the slower cyclist "x-2" (since we know the slower cyclist travels at 2 mi/h slower).
We know that they are traveling in opposite directions, so we can add their rates together to find the total distance traveled: x + (x-2) = 2x - 2.
We also know that after 3 hours, they are 123 miles apart, so we can set up the equation: 3(x + x-2) = 123.
Simplifying this equation gives us: 6x - 6 = 123, which we can solve for x: 6x = 129, x = 21.5.
So the faster cyclist is traveling at a rate of 21.5 mi/h, and the slower cyclist is traveling at a rate of 19.5 mi/h.
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1. Determine the energy released per kilogram of fuel used.
Given MeV per reaction, calculate energy in joules per kilogram of reactants.
Consider 1 mole of tritium plus 1 mole of deuterium to be a mole of “reactions” (total molar mass = 5 grams).
2. Determine the mass of fuel required for the expected energy consumption in the United States for the next 10 years.
Energy use per person per year in the United States = 3.5 × 1011 joules.
Base your calculations on a current population of 310,000,000.
1MeV = 1.6 x 10-13 J and 3.5 x 1011 joules of energy is energy in joules per kilogram of reactants.
The amount of fuel needed to meet US expectations for energy consumption over the next ten years.
In the US, each person uses 3.5 x 1011 joules of energy annually. 310,000,000 people make up the present population, thus use 1MeV = 1.6 x 10-13 J in your calculations.
In the US, annual energy consumption per person is equal to 3.5 x 1011Joules (estimated, varies by source, August 2009)
USA population: 310,000,000, roughly.
One mega electron volt, or one million electron volts, is designated as MeV. A particle with one electron charge will gain one MeV of energy when it passes through a potential difference of one million volts in a vacuum.
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How much longer (percentage) is a one-mile race than a 1500-m race (""the metric mile"")?
Answer:
1 m = 39.37 in = 3.281 ft
1500 m * 3.281 ft / m = 4922 ft
(5280 - 4922) / 4922 = .073 = 7.3 %
(Note - 1600 m often replaces the 1 mi run)
Gravity follows an inverse square law. This means that if the distance between two masses is decreased by a factor of 4, the gravitational force between those two masses:________
A. increases by a factor of 4.
B. increases by a factor of 2.
C. increases by a factor of 16.
D. decreases by a factor of 4.
E. decreases by a factor of 16.
Gravity follows an inverse square law. This means that if the distance between two masses is decreased by a factor of 4, the gravitational force between those two masses: C. increases by a factor of 16.
Gravitational force is an attractive force that exists between all objects with mass; an object with mass attracts another object with mass; the magnitude of the force is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between the two objects.
Force between two masses = G M1 M1 / [tex]R^{2}[/tex]
since , gravitation force d follows an inverse square law
F is directly proportional to 1/[tex]R^{2}[/tex]
If distance between two masses is decreased by a factor of 4
Let initial distance : R
when distance between two masses is decreased by a factor of 4 = 4R
Force = G M1 M1 / [tex](4R)^{2}[/tex]
Force = G M1 M1 / [tex]16R^{2}[/tex]
16 Force = G M1 M1 / [tex]R^{2}[/tex]
since , there is an inverse relation , so if distance is decreased , gravitation force will increase .
hence, gravitational force will increase by factor of 16
correct option C. increases by a factor of 16.
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Which of the following areas takes visual information from one side of the body and conveys it to the opposite side
The optic chiasm is the point where the optic nerves cross the midline, allowing the opposite side of the brain to process sensory data from one side of the body.
What is the optic chiasm and where is it located?Since the optic nerves cross in the optic chiasm, also known as the optic chiasma, it plays a crucial role in the visual pathway. Within the suprasellar cistern, it is situated 10 mm above the pituitary gland and 10 mm beneath the hypothalamus near the base of the brain.
The optic chiasm's function is to make sure that visual impulses reach both hemispheres of the brain. The thalamus receives and processes the majority of brain impulses, which are then transmitted to various parts of the occipital lobe. Half of each divided optic nerve's fibers travel to the opposing side. Due to the anatomical configuration, injury to the optic nerve system results in particular patterns of vision loss.
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The spectral type of this star is B7V. The order of spectral types, from hottest to coolest, is OBAFGKM. How does the surface temperature of this star compare with the other stars we have observed
The hottest celebrity is this one.
The majority of stars fall under a select few spectral categories. The hottest to the coldest stars are listed in the spectral types of the Henry Draper and Bright Star Catalogues (see stellar classification). The letters O, B, A, F, G, K, and M are used to indicate these categories in decreasing order of temperature.
What is Spectral type of star ?Using spectral types, we can categorise stars based on their colour or the spectral lines that are visible in their light. The spectral types are OBAFGKM, with the hottest stars being O and the coldest being M. To humans, cooler stars appear redder and hotter stars appear bluer.
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Three charges, qA is +6.0 μC, qB is –5.0 μC, and qc is +6.0 μC, are located at the corners of a square with each
side length at 5.0 cm as shown in the diagram. Calculate the electric field at point D.
The net electric field at point D is determined as 3.95 x 10⁷ N/C.
Electric field at D due to charge A
E = kq/r²
where;
r is the distance between A and Dq is charge AE(AD) = (9 x 10⁹ x 6 x 10⁻⁶)/(0.05²)
E(AD) = 2.16 x 10⁷ i N/C
Electric field at D due to charge B
E = kq/r²
where;
r is the distance between A and Bq is charge Br² = 5² + 5²
r² = 50
r = √50
r = 7.07 cm
E(BD) = (9 x 10⁹ x 5 x 10⁻⁶)/(0.0707²)
E(BD) = 9 x 10⁶ N/C
in x - direction = 9 x 10⁶ N/C x cos(45) = 6.36 x 10⁶ i N/C
in y - direction = 9 x 10⁶ N/C x sin(45) = 6.36 x 10⁶j N/C
Electric field at D due to charge CE = kq/r²
where;
r is the distance between C and Dq is charge CE(CD) = (9 x 10⁹ x 6 x 10⁻⁶)/(0.05²)
E(CD) = 2.16 x 10⁷ j N/C
sum of electric field in x directionEi = 2.16 x 10⁷ i N/C + 6.36 x 10⁶ i N/C
Ei = 2.796 x 10⁷ i N/C
sum of electric field in y directionEj = 2.16 x 10⁷ j N/C + 6.36 x 10⁶j N/C
Ej = 2.796 x 10⁷ j N/C
Resultant electric field at DE = √Ei² + Ej²
E = √[(2.796 x 10⁷)² + (2.796 x 10⁷)²]
E = 3.95 x 10⁷ N/C
Thus, the net electric field at point D is determined as 3.95 x 10⁷ N/C.
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A toy car is placed at 0 on a number line. It moves 9 cm to the left, then 4 cm to the right, and then 6 cm to the left. What is the total distance the toy car traveled?
1 cm
5 cm
11 cm
19 cmis the displacement of an object during a specific unit of time.
The total distance the toy car traveled is D. 19cm
Calculations and ParametersThe total distance of the toy car traveled in cm would be calculated
We would add the sum:
D = 9 + 4 + 6 cm
D = 19 cm
Therefore, the total distance the toy car traveled in cm is 19 cm.
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A 36.5-g glass thermometer reads 23.6 ∘C before it is placed in 145 mL of water. When the water and thermometer come to equilibrium, the thermometer reads 40.8 ∘C. Ignore the mass of fluid inside the glass thermometer. The value of specific heat for water is 4186 J/kg⋅C∘, and for glass is 840 J/kg⋅C∘.
The initial temperature of the water was [tex]41.6688^{0} C[/tex].
Given,
Weight of glass 36.5g
specific heat for glass is 840 J/kg⋅C∘.
Initial temperature of glass was [tex]23.6^{0} C[/tex].
Weight of water is 145*1=145g (Density*Volume=145ml*1g/ml)
Temperature final was [tex]40.8^{0} C[/tex].
specific heat for water is 4186 J/kgâ‹…Câˆ
(m of glass)(Cp of glass)(Tf_glass-Ti_glass) = (m of water)(Cp of water)(Ti_water - Tf_water)
36.5*840*(40.8-23.6)=145*4186*(Ti_water - 40.8)
Ti_water=[tex]41.6688^{0} C[/tex]
Specific heatIn thermodynamics, a material's specific heat capacity, or massic heat capacity as it is sometimes known, is equal to the heat capacity of a sample of the substance divided by the mass of the sample (symbol cp). Informally, it is the quantity of heat needed to raise a substance's temperature by one degree for every unit of mass that is added to it. joule per kelvin per kilogram, or Jkg1K1, is the SI unit for specific heat capacity. For instance, the amount of energy needed to increase the temperature of 1 kilogram of water by 1 K is 4184 joules, making water's specific heat capacity 4184 J kg 1 K 1.
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A plastic rod is charged up by rubbing a wool cloth, and brought to an initially neutral metallic sphere that is insulated from ground. It is allowed to touch the sphere for a few seconds, and then is separated from the sphere by a small distance. After the rod is separated, the rod:.
After the rod is charged and then touched on the neutral metallic sphere and then separated from it, the rod is repelled by the sphere. Option A
What is a static charge?There are very ways in which a static charge could be built up in an object. The ways include;
FrictionElectrostatic induction and ContactNow, after the rod is charged and then touched on the neutral metallic sphere and then separated from it, the rod is repelled by the sphere.
Missing parts;
A plastic rod is charged up by rubbing a wool cloth, and brought to an initially neutral metallic sphere that is insulated from the ground. It is allowed to touch the sphere for a few seconds, and then is separated from the sphere by a small distance. After the rod is separated, the rod
A. is attracted by the sphere
B. is repelled by the sphere
C. feels no force due to the sphere
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Describe and explain your observations using the law of conservation of charge and the properties of the conductors.
What is Law of conservation of charge?
Law of conservation of charge states that, "the total electric charge in an isolated system is always constant".
It can also be stated as, "Charge can neither be created nor destroyed but can only be converted from one form of energy to another".
What are the properties of conductors?
There is movement of electrons and ions in the conductor. Free charges exist on the surface of the conductor.The charge density of a conductor is zero.All points of a conductor are at the same potential.The electric field of a conductor is zero. This allows the electrons to flow within them.To learn more about Law of conservation of charge: https://brainly.com/question/4158552
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What must the charge (sign and magnitude) of a 3.45 g particle be for it to remain stationary when placed in a downward-directed electric field of magnitude 590 N/C
charge must be equal to 5.74 ×10⁻⁵
In the question it is said that the particle remains stationary which means the the net force on the particle is zero. So, the counterbalancing forces must be equal which means weight is equal to upward electric force.
→ Fnet =0
→ mg = qE
substituting the values we get :
0.00345 × 9.81 = q × 590
→ q = 5.74 ×10⁻⁵
Hence the charge must be equal to 5.74 ×10⁻⁵.
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Pearl labels a diagram of a charged capacitor as shown. Which change would correct the error in the diagram?
A) changing +2Q to +Q
B) changing +2Q to –2Q
C) reversing the direction of the arrows
D) reversing the labels for Conductors and Insulator
To correct the error in the diagram, we need to change +2Q to +Q in order for the charges to become balanced. Option A
What is a capacitor?A capacitor is device that is used for storing electric charge. We know that the capacitor is composed of two conductors separated by an insulator.
In order to correct the error in the diagram, we need to change +2Q to +Q in order for the charges to become balanced. Option A
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Answer:
A
Explanation:
In the simulation, select the pressure tab, then select the right-most of the three reservoir configurations (top left). By putting weights into the small column of water and using the pressure gauge to measure the water and air pressure, estimate the cross-sectional area of the left column of water. Which of the following best represents the cross-sectional area
The volume of any rectangular solid, including a cube, is calculated mathematically as V = l × w × h
How to find a cross-sectional area?In a given calculation, if you are given the:
Length WidthHeightTo find this, you would have to use the area of its base which is:
Length * Width * Height.
Furthermore, if the cross-section is parallel, then you would have to solve it thus:
Length * Width which is the area of the section from top to bottom.
Although your question is incomplete, the general idea of how to find the cross-sectional area of the volume of any rectangular solid.
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what is the frequency of a wave that has a wavelength of 0.20m and a speed of 22 m/s?
Answer:
f=110HZ
Explanation:
Calculate the frequency of a wave
Based on equation λ= VT but T= 1/f
=> λ=V/f
=> f= V/λ
by V=22m/s
λ= 0.20m
=> f= 22/0.20= 22/(2×10-¹) = 110Hz
So the frequency of a wave is f=110Hz
Answer:
110
Explanation:
velocity=wavelength×frequency
22=0.20f
divide both sides by 0.20
22/0.20=0.20f/0.20
f=22/0.20
f=110
The spectral type of this star is listed as K5V. (V means it is a main sequence star.) Based on the table below, how does the surface temperature of this star compare with that of HIP 87937
It turns out that the star in question belongs to the K5V star class. Thus, the surface temperature of this must be between 5200 K and 3700 K. It has a surface temperature of 6200 K to 5200 K and is a G2V class star, commonly known as Bernard's star. In other words, the star in question has a colder surface than HIP 87937. This is further explained below.
What is surface temperature?Generally, The temperature at a surface is referred to as the surface temperature. In particular, it may refer to the surface air temperature, which is the temperature of the air that is relatively close to the earth's surface.
In conclusion, The star in question is of the K5V type. Therefore, the temperature of the surface of this must be somewhere between 5200 and 3700 kelvin. The star with the designation HIP 87937, often known as Bernard's star, is of the G2V type. Stars of this type have a surface temperature that falls anywhere between 6200 and 5200 degrees Celsius. Therefore, it should come as no surprise that the surface temperature of the given star is lower than that of HIP 87937.
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Answer: It is hotter because K is before M
Explanation:
The actual surface temperature of this star is 4600 KK compared to 3100 KK for the M4 star in Parts A and B.
A stone ‘X’ of mass 2 kg is at the height of 20m in two minutes, calculate the power delivered. [g=10 m/s-2]
400 J power will be delivered by lifting a stone of mass 2 kg at the height of 20m in two minutes.
What is power?The quantity of energy transferred or transformed per unit of time is known as power. The watt, or one joule per second, is the unit of power in the International System of Units. Power is also referred to as an activity in ancient writings. A scalar quantity is a power.
Work completed and time is linked in the power equation. Since forces may move objects and we know that forces perform work, we might anticipate that by understanding the power, we can gain insight into how a body moves through time. This outcome may be especially beneficial.
Given that, a stone ‘X’ of mass 2 kg is lifted to the height of 20m in two minutes, and g=10 m/s-2
Power Delivered = Work done in lifting the stone
Work Done = Potential energy = mgh
Work done = 2 × 10 × 20
Work done = 400 J
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A long narrow solenoid has length l and a total of N turns, each of which has cross-sectional area A. Its inductance is:
A long narrow solenoid has length l and a total of N turns, each of which has cross-sectional area A. Its inductance is μ₀ ( [tex]\frac{N^2A}{l}[/tex] ).
To find the answer, we need to know about the magnetic field due to a solenoid.
What is the magnetic field due to a solenoid?A solenoid is an insulated wire wound in the form of a helix. Its length is very large compared to its diameter.The magnetic field due to solenoid carrying current [tex]I[/tex] can be written as,[tex]B=[/tex] μ₀n [tex]I[/tex]
[tex]n=\frac{N}{l}[/tex]
We have an expression for magnetic flux as,Φ [tex]= BA[/tex] Where, A is the area.
Substituting above value of magnetic field in the expression of magnetic flux, we get,Ф [tex]= \frac{NIA}{l}[/tex] μ₀
In terms of inductance, we can express the magnetic flux linked with the coil as,Ф [tex]= LI[/tex]
By equating above two equations of magnetic flux, we get the expression for inductance as,μ₀ ( [tex]\frac{N^2A}{l}[/tex] ) [tex]I[/tex] [tex]=LI[/tex]
[tex]L=[/tex] μ₀ ( [tex]\frac{N^2A}{l}[/tex] ).
Thus, we can conclude that the expression for inductance is μ₀ ( [tex]\frac{N^2A}{l}[/tex] ).
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The inductance of a solenoid having N number of turns, area A and a length l will be equal to μ₀ ( [tex]\frac{N^2A}{l}[/tex]).
We need to understand the magnetic field created by a solenoid in order to determine the solution.
What does a solenoid's magnetic field look like?An insulated wire twisted into a helix is what makes up a solenoid.Compared to its diameter, its length is significantly larger.It is possible to express the magnetic field caused by a solenoid carrying current as,[tex]B=\frac{NI}{l}[/tex]×μ₀
We can express magnetic flux as follows:[tex]flux=BA[/tex] , A is the area.
In the formula for magnetic flux, we obtain by substituting the above magnetic field value:[tex]flux=\frac{NIA}{l}[/tex] times the μ₀.
The magnetic flux associated with the coil can be expressed in terms of inductance as follows:[tex]flux=IL[/tex]
We obtain the expression for inductance as, by combining the aforementioned two magnetic flux equations.μ₀ ( [tex]\frac{N^2AI}{l}[/tex])= [tex]LI[/tex]
[tex]L=[/tex] μ₀ ( [tex]\frac{N^2A}{l}[/tex]).
As a result, we can say that the inductance expression is [tex]L=[/tex] μ₀ ( [tex]\frac{N^2A}{l}[/tex]).
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A uniform bar 15m long balanced on a pivot at its midpoint. A boy of mass 55kg sits on one arm of the bar at a point 5m away from the pivot. What mass can be placed 2m away from the other end of the bar to keep the bar horizontally
The mass at the other end of bar will be 50g .
what is mass
It is the fundamental property of matter , every single property which exist in this world has mass
Mass never can be 0 .
So , the system is in equilibrium
let mass of the body be m
55×5= m×5.5
m= 5 5 × 5 /. 5.5
m= 5 0g
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137.5 kg mass can be placed 2m away from the other end of the bar to keep the bar horizontally.
What does horizontal mean?Any straight line traveling from left to right or right to left is a horizontal line. If two points on a line share the same Y-coordinates, the line is said to be horizontal in coordinate geometry. It is derived from the word "horizon." In other words, the horizon or x-axis is always parallel to the horizontal lines.In the coordinate plane, a horizontal line is a straight line drawn from right to left or from left to right, perpendicular to the x-axis. In other words, a horizontal line is a straight line with an intercept solely on the y-axis, not the x-axis.To keep the bar horizontal, the right and left side torques must be equal:
[tex]F_{1} d_{1} =F_{2} d_{2}[/tex]
[tex]F_{2} =F_{1} \frac{d_{1} }{d_{2} }[/tex]
[tex]=(55.9.8)\frac{5}{2}[/tex]
=1347.5 N.
Convert this force of gravity into mass:
[tex]F_{2} =m_{2} g,[/tex]
[tex]m_{2} =\frac{F_{2} }{g}[/tex]
[tex]=\frac{1347.5}{9.8}[/tex]
=137.5 kg.
The answer is 137.5 kg.
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According to the theory of a symmetry breaking, at the moment of quark confinement, when the universe was 10-6 seconds old, what were the relative numbers of neutrons and antineutrons
At the time of quark confinement, when the universe was 10-6 seconds old, there is found to be one additional proton for every billion antiprotons.
What is quark confinement?Note that one quark is never found on its own but if particles are said to be smashed together and quarks are found, they are said to be like ends of rubber bands that expands.
Hence, At the time of quark confinement, when the universe was 10-6 seconds old, there is found to be one additional proton for every billion antiprotons.
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A 7.55 × 1014 hz electromagnetic wave travels in carbon tetrachloride with a speed of 2.05 ×108 m/s. what is the wavelength of the wave in this material?
Answer:
2.72×10^-7
Explanation:
velocity = frequency × wavelength
2.05×10^8=7.55×10^14 wavelength
wavelength = 2.05×10^8/7.55×10^14
wavelength = 2.72×10^-7
A train is traveling at 30.0 m/sm/s relative to the ground in still air. The frequency of the note emitted by the train whistle is 262 HzHz. The speed of sound in air should be taken as 344 m/sm/s .
frequency fapproach is heard by a passenger = 302.05 Hz
frequency frecede is heard by a passenger = 228.37433 Hz
Given :
speed of train to the ground = 30.0 m/s
frequency emitted by the train whistle = 262 Hz
speed of sound in air = 344 m/s
To Find :
(A) frequency fapproach (B) frequency frecede
Solution :
The frequency of approach is given by
f' = f v + v(relative)
v - v(air)
= 262x 344 + 18
344 - 30
f' = 302.05 Hz
The frequency of approach is 302.05 Hz
The frequency of recede is given by
f' = f v - v(relative)
v + v(air)
= 262 x 344 - 18
344 + 30
The frequency of recede is 228.37433 Hz
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Radiation in the ultraviolet region of the electromagnetic spectrum is quite energetic. It is this radiation that causes dyes to fade and your skin to develop a sunburn. If you are bombarded with 1. 00 mol of photons with a wavelength of 370. Nm, what amount of energy, in kilojoules per mole of photons, are you being subjected to? energy mol submit answer try another versiorn 2 item attempts remaining.
The energy of photon in kJ/mol is 329kJ/mol.
Wavelength of radiation is 370nm. The frequency of given wavelength is
ν = c / λ
ν = 3×10^8 / 370×10^-9
ν = 8.11 × 10^14 s^-1
Now the energy of photon is:
E = hν
E = 6.63×10^-34 J.s/photon × 8.11×10^14s^-1
E = 5.41× 10^-19 J/photon
To find in mole
E = 5.41× 10^-19 × 6.022×10^23
E = 3.29 ×10^ 5 J/mol
So, the energy of mole of photon is equal to 329 kJ/mol.
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A projectile is fired in such a way that its horizontal range is equal to three times its maximum height. What is the angle of projection
The angle of projection is θ = 53°
What is the angle of projection?The angle between the initial velocity of a body from a horizontal plane through which the body is thrown, is known as angle of projection.Motion in A Plane. Show that there are two angles of projection for which horizontal range is the same. Thus horizontal range is the same for angle of projection θ and α = 90°–θ.The maximum height achieved by a projectile ignoring the air resistance is given by HM=U2Sin2 θ 2g.where U is the initial velocity, θ is the angle of projection and g is the acceleration due to gravity.
R = 3H
R = v²sin2θ/g = 2v²sinθcosθ/2 = 3v²sin²θ/2g
tan θ = 4/3
θ = 53°
So, the angle of projection is θ = 53°
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Vega, the brightest star in the constellation lyra, has a parallax angle of approximately 0.13 arcseconds. approximately how far away is vega from the sun?
Vega, the brightest star in the constellation lyra, has a parallax angle of approximately 0.13 arcseconds, approximately Vega will be 25.076 Light year or 7.692 Parsec away from the sun
The parallax angle is the angle between the Earth at one time of year, and the Earth six months later, as measured from a nearby star.
Mathematically it can be understood as that the parallax angle is the angle which is taken from a point at one time on the earth and again after six months later from the same point on the earth. The parallax angle is the semi-angle of inclination between the two lines to sight.
Stellar parallax is the basis for the parsec, which is the distance from the Sun to an astronomical object that has a parallax angle of one arcsecond.
Distance (in parsec) = 1 / (parallax angle ( arcsec))
given
parallax angle = 0.13 arcseconds
Distance (in parsec) = 1/ 0.13 = 7.692 Parsec
if 1 Parsec = 3.26 Light year
So, 7.692 Parsec will be equal to = 3.26 * 7.692 = 25.076 Light year
≈ 25.076 Light year
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A 540 gram object is attached to a vertical spring, causing the spring’s length to change from 70 cm to 110 cm.
What is the spring constant k?
Group of answer choices
130 N/m
33 N/m
13 N/m
330 N/m
Answer:
Approximately [tex]13\; {\rm N \cdot m^{-1}}[/tex] (assuming that [tex]g = 9.81\; {\rm N \cdot kg^{-1}}[/tex].)
Explanation:
Let [tex]F_{\text{s}}[/tex] denote the force that this spring exerts on the object. Let [tex]x[/tex] denote the displacement of this spring from the equilibrium position.
By Hooke's Law, the spring constant [tex]k[/tex] of this spring would ensure that [tex]F_\text{s} = -k\, x[/tex].
Note that the mass of the object attached to this spring is [tex]m = 540\; {\rm g} = 0.540\; {\rm kg}[/tex]. Thus, the weight of this object would be [tex]m\, g = 0.540\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \approx 5.230\; {\rm N}[/tex].
Assuming that this object is not moving, the spring would need to exert an upward force of the same magnitude on the object. Thus, [tex]F_{\text{s}} = 5.230\; {\rm N}[/tex].
The spring in this question was stretched downward from its equilibrium by:
[tex]\begin{aligned} x &= (70\; {\rm cm} - 110\; {\rm cm}) \\ &= (-40)\; {\rm cm} \\ &= (-0.40) \; {\rm m}\end{aligned}[/tex].
(Note that [tex]x[/tex] is negative since this displacement points downwards.)
Rearrange Hooke's Law to find [tex]k[/tex] in terms of [tex]F_{\text{s}}[/tex] and [tex]x[/tex]:
[tex]\begin{aligned} k &= \frac{F_{\text{s}}}{-x} \\ &\approx \frac{5.230\; {\rm N}}{-(-0.40)\; {\rm m}} \\ &\approx 13\; {\rm N \cdot m^{-1}}\end{aligned}[/tex].
Consider vectors u and v, where u = ⟨1, –1⟩ and v = ⟨1, 1⟩. what is the measure of the angle between the vectors?
The angle between the two vectors is 0⁰, thus the two vectors are parallel to each other.
Angle between the vectorsThe angle between the vectors describes the direction of the vector and the value of the angle can be determined from the horizontal and vertical components of the vectors as shown below.
The sum of the horizontal components and vertical components of the vectors is calculated as follows;
Sum of the horizontal component of the vectors, x = 1 + 1 = 2
Sum of the vertical component of the vectors, y = -1 + 1 = 0
The angle between the vectors is calculated as follows;
θ = arc tan (y/x)
θ = arc tan (0/2)
θ = arc tan (0)
θ = 0⁰
The angle between the two vectors is 0⁰, thus the two vectors are parallel to each other.
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Answer: C. 90°
Explanation:
A force does work on an object if a component of the force __________.
Group of answer choices
a. is parallel to the displacement of the object
b. is perpendicular to the displacement of the object
c. perpendicular to the displacement of the object moves the object along a path that returns to its starting point
d. parallel to the displacement of the object moves the object along a path that returns to its starting point
Option A. A force does work on an object if a component of the force is is parallel to the displacement of the object.
Work done by force
The force applied to an object to displace it from a given point to another point is known as work done on the object.
W = Fd cosθ
where;
f is the magnitude of applied forced is the displacement of the object.θ is the angle between the applied force and displacement.Thus, A force does work on an object if a component of the force is is parallel to the displacement of the object.
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A 100-lb child stands on a scale while riding in an elevator. What does the scale read while the elevator slows to stop at the lowest floor
Answer: A 100-lb child stands on a scale while riding in an elevator. Then, the scale reading approaches to 100lb, while the elevator slows to stop at the lowest floor
Explanation: To find the correct answer, we need to know more about the apparent weight of a body in a lift.
What is the apparent weight of a body in a lift?Consider a body of mass m kept on a weighing machine in a lift.The readings on the machine is the force exerted by the body on the machine(action), which is equal to the force exerted by the machine on the body(reaction).The reaction we get as the weight recorded by the machine, and it is called the apparent weight.How to solve the question?Here we have given with the actual weight of the body as 100lbs.This 100lb child is standing on the scale or the weighing machine, when it is riding .During this condition, the acceleration of the lift is towards downward, and thus, a force of ma .There is also mg downwards and a normal reaction in the upward direction.when we equate both the upward force and downward force, we get,[tex]ma=mg-N\\N=mg-ma[/tex] i.e. during riding the scale reads a weight less than that of actual weight.
When the lift goes slow and stops the lowest floor, then the acceleration will be approaches to zero.Thus, from the above explanation, it is clear that ,when the elevator moves to the lowest floor slowly and stops, then the apparent weight will become the actual weight.
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A convex lens has a focal length f. An object is placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. The image is located at what distance from the lens
The image formed will be located between the focal point, f and double of the distance from focal point, 2f.
What is convex lens?A convex lens is the name given to any converging lens.
A converging lens or convex lens is a lens that converges rays of light that are traveling parallel to its principal axis.
What is focal length?The focal length, f of a lens is the distance between the center of a lens and its focus.
Object placed between infinity and 2fFor an object that is placed between infinity and double of the distance from focal point, along a line perpendicular to the center of the lens,
The image formed will be located between the focal point, f and double of the distance from focal point, 2f.
Thus, for an object placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. The image formed will be located between the focal point, f and double of the distance from focal point, 2f.
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When a person is standing upright, the weight of anything being lifted and carried in the hands is first reflected onto the:
Pelvic girdle
In human anatomy, the pelvis is a complex of bones that connects the trunk and the legs, supports and balances the trunk, and houses and supports the intestines, the urinary bladder, and the internal organ. It is sometimes referred to as the bony pelvis or the pelvic girdle.
One is located on the left side of the body and the other is located on the right. They come together to make the pelvic girdle, a portion of the pelvis. The hip bones are attached to the upper portion of the skeleton at the sacrum.
The pelvic girdle's main function is to support the upper body's weight while seated and transfer that weight to the lower limbs while standing. For the muscles in the trunk and lower limbs, it functions as attachment point.
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