Answer:
B
Explanation:
it has the best view for seeing the shape of the arm in a spiral galaxy
The type of view would best allow scientist to see the shape of the arm in a spiral galaxy is Side diagnol.
What is Spiral galaxy?Spiral galaxies are twisted collections of stars and gas that often have beautiful shapes and are made up of hot young stars.
Most of the galaxies that scientists have discovered so far are spiral galaxies, as opposed to the other two main categories of galaxy shapes — elliptical and irregular. The Milky Way – the galaxy that includes Earth and our solar system – is an example of a spiral galaxy.
The majority of spiral galaxies have a flat, spinning disk of stars around a central bulge. Older, fainter stars make up the bulge in the center, which is thought to house a supermassive black hole.
Therefore, The type of view would best allow scientist to see the shape of the arm in a spiral galaxy is Side diagnol.
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A copper rod of length 0.77 m is lying on a frictionless table (see the drawing). Each end of the rod is attached to a fixed wire by an unstretched spring that has a spring constant of k = 76 N/m. A magnetic field with a strength of 0.14 T is oriented perpendicular to the surface of the table.
(a) What must be the direction of the current in the copper rod that causes the springs to stretch?
The current flows (left-to-right/right-to-left) in the copper rod.
(b) If the current is 14 A, by how much does each spring stretch?
________ m
Answer:
a) The direction of the current in the copper rod that causes the springs to stretch is left-to-right. This is because the magnetic field is oriented perpendicular to the surface of the table and the force exerted on the rod by the magnetic field is given by F = qVB, where F is the force, q is the charge of the particle, V is the velocity of the particle, and B is the strength of the magnetic field. Since the force is perpendicular to the velocity of the particle, the direction of the current that produces this force must be parallel to the magnetic field. In this case, the magnetic field is oriented perpendicular to the surface of the table, so the current must flow in the direction left-to-right to produce a force that stretches the springs.
b) To find by how much each spring stretches, you can use the formula F = kx, where F is the force exerted by the spring, k is the spring constant, and x is the distance the spring stretches. In this case, the force exerted by the spring is given by F = qVB, and the spring constant is k = 76 N/m. The charge of the particle is q = Ie, where I is the current and e is the charge of an electron. The velocity of the particle is V = L / t, where L is the length of the rod and t is the time it takes the particle to travel the length of the rod. Since the current is 14 A and the length of the rod is 0.77 m, the velocity of the particle is V = 0.77 m / (1 / 14 A) = 10.78 m/s. The strength of the magnetic field is 0.14 T, so the force exerted by the spring is F = (14 A)(1.60 x 10^-19 C)(10.78 m/s)(0.14 T) = 2.40 x 10^-17 N. Therefore, the distance each spring stretches is x = F / k = 2.40 x 10^-17 N / 76 N/m = 3.16 x 10^-19 meters.
How do you prevent latency problems?
Latency problems can be prevented by not downloading multiple items at a time, not running multiple applications simultaneously, scanning for viruses, and not deleting the cache.
What causes latency problems?One of the principal causes of network latency is distance, specifically the distance between client devices making requests and the servers responding to those requests. Customers demand to communicate with technology in real time without any delays, hence low latency is essential. Users may stop using a platform altogether and switch to another application permanently if there are problems with severe latency and time delays.
How is latency measured?In milliseconds, latency reveals the strength of your connection within your network. For gaming, anything with a latency of 100ms or less is fine. However, the ideal range is 20–40 ms.
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A soft drink bottle resonates as air is blown across its top. What happens to the resonant frequency as the level of fl uid in the bottle decreases
As air is blowing across the top of a soft drink bottle, it reverberates. The frequency grows as the chamber's length lengthens.
Who defines frequency?The frequency of physics is the number of waves that pass by a specific location in a time period. According to this concept, how several cycles or waves do a body in periodical motion experience in a single unit of time?
What is a wave length?The distance between normal incidence (adjacent crests) in adjacent cycles determines how far a waveform signal has traveled in place or over a wire. In wireless systems, this length is often expressed in metres (m), centimeters (cm), or millimeters (mm) (mm).
Therefore, As air is blown, a soda pop bottle reverberates.
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The scale on a map states that 1 centimeter corresponds to 20 kilometers. On the map, two cities are 0.3 cm apart. Find the actual distance.a.6 kmc.0.6 kmb.600 kmd.60 km
The actual distance is 6 km. The solution to the problem is as follows: By ratio and proportion: 1:20 = 0.3:x, Cross multiplying: 20(0.3) = x, x = 6
Therefore the answer is the first choice or letter A which is 6 km.
How would a surface without friction feel?It just seems slick, almost like touching ice but without the frigid sensation, according to my firsthand experience of both. Sorry, it's really nothing exceptional. Any surface would be sufficient if it had some lubrication oil on it.
Is there any surface in the world without friction?In reality, there are no frictionless planes. If they did exist, items on them would almost certainly behave exactly as Galileo predicted if they did. Despite not existing, they are extremely valuable for designing things like engines, motors, roads, and even tow truck beds, to mention a few.
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Is it possible to whirl a bucket of water fast enough in a vertical circle so the water won't fall out if so, what is the minimun speed
Yes, it is possible to whirl a bucket of water fast enough in a vertical circle so the water won't fall out.
The minimum speed required to do this is known as the “Centrifugal Force Limit” and is calculated based on the size and shape of the bucket and the weight of the water. Generally, a speed of at least 20-30 revolutions per minute is required to keep the water from spilling out.
F = (m * v^2) / r
Where:
F = centrifugal force (N) m = mass of water (kg) v = linear velocity (m/s) r = radius of the circle (m)Learn more about speed:
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2.71 m and 4.4 m long and have masses of 69.5 kg and 100 kg, respectively. Calculate the total rotational kinetic energy of the two hands about the axis of rotation. Model the hands as lon
Answer:
1.04 x 10-3 J.
Explanation:
The total rotational kinetic energy of the two hands about the axis of rotation is calculated using the formula:
Kinetic Energy = 1/2 I ω2,
where I is the moment of inertia and ω is the angular velocity.
For this scenario, the moment of inertia is calculated by
I = 1/3 ML2,
where M is the total mass and L is the length of the arm.
Since the total mass of the two hands is 169.5 kg, and the length of the arms is 2.71 m and 4.4 m, the moment of inertia is calculated to be I = 5.35 x 10-5 kg m2. Substituting this value of I into the equation, the total rotational kinetic energy of the two hands about the axis of rotation is calculated to be 1.04 x 10-3 J.
Using the conductor sizing guide, what conductor ampacity is needed for a 10-horsepower, 230-volt, single-phase motor: a.50 A
b.60 A
c.62.5 A
d.87.5 A
The correct conductor ampacity for a 10-horsepower, 230-volt, single-phase motor is option c. 62.5 A.
The ampacity of a conductor is a measure of the maximum amount of electrical current that can flow through it safely. The ampacity required for a motor is based on the size of the motor and the voltage of the electrical system. There are standard methods for determining the minimum ampacity for a given motor and voltage, such as the National Electric Code (NEC) and the American National Standards Institute (ANSI). The NEC and ANSI both state that the minimum ampacity for a 10-horsepower, 230-volt, single-phase motor is 62.5 amperes. It's important to note that using a conductor with ampacity lower than the recommended one may cause the motor to overheat and fail, leading to damage or even fire hazard.
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If it takes 4 hours for the Hogwarts express, moving at a speed of 100 mi/hr,to make it from Platform 9 and 3/4 to Hogwarts,how far apart are they?
The distance between Platform 9 and 3/4 and Hogwarts at a speed of 100miles/hour is 400miles.
What is distance?Distance is defined as an object's total movement with or without regard for direction. Distance can be defined as how much ground an object has covered regardless of its starting or ending point. Distance can be measured as Speed multiplied by Time.
If it takes 4 hours from Hogwarts express, at a speed of 100mi/hr to Platform 9 and 3/4 to Hogwarts, using the formula;
Distance = Speed x Time
Distance = 100 miles/hour x 4 hours
Distance = 400 miles
Therefore, the distance to platform 9 and 3/4 from Hogwarts express is 400 miles.
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What is the charge Q on the capacitor immediately after the switch is moved to position b?
Express your answer using two significant figures.
Answer must be in microC.
18 μC is the charge Q on the capacitor immediately after the switch is moved to position b .
The expression for the charge on the capacitor is as follows :
Q = CV
substitute 2.0 μF for C and 9V for V.
Q = (2μF) {[tex]\frac{1 * 10^{-6} F }{1μF}[/tex]} (9V)
= 18 * [tex]10^{-6}[/tex] C
≈ 18 μC
Charge is not stored in capacitors. In reality, capacitors store an unbalanced charge. If a capacitor's one plate has one coulomb of charge stored on it and the other plate has one less, the total charge (added up over both plates) will be zero.
Formula q=CV, where q is the charge stored, C is the capacitance, and V is the applied voltage, describes this relationship.
Always, current flows from -ve to +ve. As a result, charge will move away from the -ve plate and towards the +ve plate. Therefore, the charge on a capacitor always equals the charge on the positive plate, never the negative.
The link between a capacitor's capacitance, its charge, and the voltage across it.
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A proton accelerates from rest in a uniform electric field of 660 N/C. At one later moment, its speed is 1.10 Mm/s (nonrelativistic because v is much less than the speed of light). (a) Find the acceleration of the proton. .81 Incorrect: Your answer is incorrect. m/s2 (b) Over what time interval does the proton reach this speed
Q is the charge's magnitude, V is its velocity, X is the angle formed by the magnetic field's direction and the charge's motion, and B is the strength of the magnetic field.
We must divide this amount by the mass of the charged particle or particles in order to determine the acceleration. Its speed at a later time is 1. 20 Mm/s (non relativistic because v is much less than the speed of light). When a refractive index diminishes over time, light shifts its frequency, which is referred to as photon acceleration [13,14]. Similar to charged particle acceleration, a rise in group velocity is accompanied by an increase in photon energy, or frequency.
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Select the correct answer. a heat engine has a cold reservoir of 250 k and a hot reservoir of 715 k. what is the maximum efficiency of the engine?
a. 65.0%
b. 60.8%
c. 73.6%
d. 58.6%
e. 69.1%
The maximum efficiency of the engine is a. 65.0%
The maximum efficiency of the heat engine is given by the Carnot efficiency, which is defined as:
Efficiency = (1 - (T cold / T hot)) * 100%
Where T cold is the temperature of the cold reservoir and T hot is the temperature of the hot reservoir.
Plugging in the given temperatures, we get:
Efficiency = (1 - (250 / 715)) * 100% = 65.0%.
So the answer is a. 65.0%.
So, using the temperatures given in the question:
Efficiency = 1 - (250 K/ 715 K) = 1 - 0.349 = 0.651 or 65.1%
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How should two resistors, with resistances R1 Ω, R2 Ω, be connected to a battery of
e.m.f. V volts so that the electrical power consumed is minimum?
Answer:
The two resistors should be connected in series.
(I assume that the question is stating the electrical power consumed by the resistors)
Explanation:
Think about the formula P = V^2 / R
For the electrical power consumed to be a minimum, we must let V be as small as possible.
For small V, between a series and a parallel connection, series is the correct connection as the combined potential difference (pd) for the two resistors is equal to the electromotive force (emf) of the battery.
However, for parallel connections, the combined pd for the two resistors is equal to twice the emf of the battery. (Each resistor will have a pd equal to the emf of the battery)
With lower total V, with the same R, power P consumed will decrease.
In the sketch to the right, a long straight wire is in the plane of a rectangular conducting wire loop. The current in the straight wire is up. At some point the current in the straight wire starts to increase in magnitude. This increased current leads to an induced current in the wire loop. In which direction will the induced current in the wire loop be? Explain how you reached this conclusion. How would your answer be different if the wire loop was on the left side of the wire instead of the right side?
The direction of the induced current in the wire loop is anti-clockwise.
The direction of the induced current if the wire loop was on the left side of the wire is clockwise.
Lenz's law and the direction of the induced current are the key concepts needed to address this issue.
To determine the direction of the induced current under various circumstances, use Lenz's law.
The induced emf of the coil is proportional to the negative of the rate of change of magnetic flux, according to Faraday's law.
The following expression represents the typical emf that is generated in the coil during the course of the time period: [tex]$$\varepsilon=-\frac{\Delta \Phi}{\Delta t}$$[/tex]
Here, [tex]$\varepsilon$[/tex] is the average emf that is induced in the coil during the time interval and [tex]$\Delta \Phi / \Delta t$[/tex] is the rate of change of magnetic flux.
A magnetic field is induced in the rectangular loop as a result of the current in the wire. The plane is the intended target of this magnetic field.
As the current in the wire grows, the magnetic flux in the rectangular coil rises.
An emf and current are induced by Faraday's law.
Following is noted from Lenz's law:
The inwards growing flux is opposed by the generated current. Therefore, the induced current must flow counterclockwise in order to meet this.
When the rectangular loop is kept to the left of the wire, the magnetic flux will be directed outward.
If the wire loop was on the left side of the wire, the induced current would flow clockwise.
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What is the role of diffusion in the dialysis process?
A concentration gradient drives the ion-exchange membrane (IEM) separation procedure known as diffusion dialysis (DD).
Diffusion dialysis is referred to be a spontaneous separation technique since the concentration gradient primarily drives the separation process. A membrane separation procedure is DD.
Diffusion is the movement of a solute along a concentration gradient through a membrane. Small molecules are eliminated in this manner during hemodialysate. Diffusion is the net transfer of a substance from a location of high concentration to a region of low concentration, according to physicists and chemists.
Diffusion in hemodialysis is formally defined as the transport of solutes as a result of random molecular motions down its concentration gradient through a semipermeable membrane. Diffusion is how most toxins are removed during dialysis.
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What is B_{\text {out }}, the z component of the magnetic field outside the solenoid?
The magnetic field outside the solenoid [tex]B_{\text {out }}[/tex] is zero.
The magnetic field lines are present outside the solenoid, but there are significantly less of them there than there are inside the solenoid. This is known as the flux. As a result, the magnetic field outside is thought to be almost nil. It is more accurate to assume that the magnetic field outside the solenoid is zero if the solenoid is quite long. It is false close to the solenoid's edge. We consider the magnetic field outside the solenoid to be zero for practical purposes. This amount of flux divided by the area outside the solenoids gives the flux density, which is equal to the strength of the field outside the solenoid is zero.
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Ball A has a mass of 3 kg and moves at a velocity of 2 m/s. Ball B has a mass of 1 kg and rolls towards Ball A with a velocity of -4 m/s. After the collision, Ball A has a velocity of -1.5 m/s. What is the velocity of ball B after the collision?
Please show your work.
The velocity of ball B after the collision is 6.5 m/s.
What is law of conservation of momentum?According to the law of conservation of momentum, The overall momentum of two or more bodies acting on one another in an isolated system stays constant unless an external force is introduced.
Before collision ,
ball A of mass of 3 kg has velocity = 2 m/s.
ball B of mass of 1 kg has velocity= -4 m/s.
After the collision,
Ball A has a velocity = -1.5 m/s.
Let Ball B has a velocity = v m/s.
Applying law of conservation of momentum,
Total initial momentum = total final momentum
3×2 +1×-4 = 3×-1.5 + 1×v
⇒ v = 3×2 +1×-4 - 3×-1.5
⇒ v = 6.5 m/s.
hence, the velocity of ball B after the collision is 6.5 m/s.
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1. Two objects with the same mass move toward each other with the same speed and experience an elastic collision. Compare the final velocities of each object to their initial velocities
Answer:
M1 U1 + M2 U2 = ( M1 + M2 ) V
Explanation:
they rebounce, therefore it's elastic.
What environmental factors can influence genetic variations?
Some harmful environmental factors can change the nucleotide sequence of a gene. UV rays, for example, can harm DNA strands.
What elements influence genetic variation?Genetic variations arise during meiosis as a result of mutation and recombination. Chemical or biological mutagens frequently result in mutations. The genetic diversity of organisms is also altered by accidental mating.
What are five examples of environmental variations?The length at which you want to wear your hair. Scars – from your own unique accidents. The strength of your muscles depends on how much exercise you get. Piercings, whether you decide to have them or not. Mutations are the primary cause of the emergence of genetic variation.
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You are deigning another dolly andbag ytem for a different actor in the performance the ma of the dolly and the actor combined i 76kg and then ma of the andbag i 18kg the coefficient of kinetic friction Between the dolly and the tage floor i 0. 20. What i the acceleration
The acceleration of a dolly-sandbag system when mass and coefficient of kinetic friction is given is calculated to be 0.29 m/s².
Given that,
The mass of the dolly and actor combined M = 76 kg
The mass of the sandbag m = 18 kg
The coefficient of kinetic friction between the dolly and the stage floor = 0.20.
Let the acceleration is a.
From Newton's 2nd law of motion, we can write that,
ΣF = (m+M) a
mg - μMg = (m+M) a
a = g (m- μM)/ (m+M)
a = 9.8 ( 18 - 0.20×76)/(18+76)
a = 0.29 m/s².
Thus, the acceleration of the dolly-sandbag system is 0.29 m/s².
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1. A force of 60 Newtons is applied to the end of a wrench 0. 12 m long. How much torque is produced?
Answer: The amount of Torque produced is 7.2 Nm.
Explanation:
Given:
Force applied (F) to the end of a wrench = 60 Newton
Length of wrench = 0.12 meter
To find:
Quantity of Torque produced
Solution:
The quantity of Torque produced can be calculated from the following formula:
Ƭ = r F sin(θ)
Where,
Ƭ = Torque, r = radius, F = Force, (θ) = angle between F and the lever arm
In the given question,
r = 0.12,
F= 60,
(θ)= 900 {Since the force is applied at the end of a wrench, it must be perpendicular}
Torque (Ƭ) = 0.12* 60 * sin 900
= 7.2 m {sin 900 = 1}
Hence, in the given situation, 7.2 Nm Torque will be produced.
Does speed increase down a ramp?
The speed depends on the gravitational force acting on the object in the rolling motion of the object that is acting on it at a continuous moment rate. the speed increases at a constant rate.
Rolling motion of any object occurs when the object starts sliding in a different methods from the other objects such as when the objects starts to roll from the ramp or any other sloppy surface and it rolls down due to the gravitational force and with many other forces such as the rolling tangential force. many forces are acting on the object at the same moment and we are just seeing the gravitational force which is playing a major portion. Hence by this information we can consider that the ball accelerates at a constant rate as it moves down the slope because of the constant gravitational force acting on it in a major portion and the rolling tangential force on the object is acting in the smaller form.
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I made an imaginary planet for my dnd campaign and I would like to know how to find the orbital ditance and the ditance from the un uing the information I have gathered o far. Day Duration: 36 hour
Orbit Duration: 1. 6 Earth year
Year Duration: 389. 3. Day
Gravity: 9. 608 m/²
Axial Preceion: 15,000 year
Axial Tilt: 21. 7 to 23. 5
Axial Ocillate: 8333. 3. Year per 0. 1 ocillate of 1. 8 ocillation
Number of moon: 3
CLimate region: much imilar to earth Temperate region are
the magority of the planet with tropical at the equator and
ubtropical at the pole with eaon changing at the prevernal,
vernal, etival, erotinal, autumnal, and hibernal period
Radiu: 4578. 2 (m)
Planet Ma: 3017387649322753000
Circumference: 28765. 6789733
The appropriate calculation is required for knowing how to find the orbital distance and the distance from the using the information.
For approximately circular orbits the orbital radius is the distance from an object in space to the body which it is orbiting. When an object orbits a body in space it rotates around that body drawing out a circle or an ellipse depending on its orbit. Earth's orbit is the path in which the Earth travels around the Sun. Earth lies at an average distance of 149.59787 million kilometers (93 million miles) from the Sun and a complete orbit occurs every 365.256 days.
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What is the function of the countercurrent system of flow?
In the renal medulla, a countercurrent mechanism keeps things in balance. The solution flows concurrently in the same direction. The solution flows in the opposite direction of the countercurrent flow.
Cross-current flow here, the liquids move in the opposing directions through the two tubes. One end of a tube in a single tube starts to flow a solution with a concentration of 0%, while the other end in the same tube starts to flow a solution with a concentration of 100%.
The kidneys have two countercurrent processes. They are the vasa recta and the Henle loop. The nephron's Henle's loop is a U-shaped structure. The two limbs of the vessel's two blood streams move in the opposing directions, creating countercurrents.
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Two negative charges of -3x10-6C exert a repulsive force of 2Non each other. By what distance are they separated?
The distance between two negative charges experiencing a force of 2 N is: 4.44 x 10^-3 m
According to Coulomb's Law, the magnitude of the electric force between two negative charges is given by:
F = k * q1 * q2 / r^2
where k is the Coulomb constant (8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between them.
Plugging in the given values, we get:
2N = 8.99 x 10^9 N m^2/C^2 * (-3 x 10^-6 C)^2 / r^2
Solving for r, we get:
r = sqrt(8.99 x 10^9 N m^2/C^2 * (-3 x 10^-6 C)^2 / 2N)
r = 4.44 x 10^-3 m
Coulomb's Law states that the magnitude of the electric force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. The constant of proportionality is known as the Coulomb constant (k). Therefore, the equation for the magnitude of the electric force is given by F = k * q1 * q2 / r^2, where k is the Coulomb constant, q1 and q2 are the charges, and r is the distance between them.
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Why would a parcel of air rise relative to other air in the atmosphere?
a. A parcel of air will rise if it has a lower density than the surrounding air.
b. A parcel of air will rise if the air in the parcel has a lower mass than the surrounding air.
c. A parcel of air will rise if it has a higher density than the surrounding air.
d. A parcel of air will rise if the air in the parcel has a higher mass than the surrounding air.
A) A parcel of air will rise if it has a lower density than the surrounding air. is the relative order of air in the atmosphere.
In the atmosphere, air moves from high pressure to low pressure areas. When a parcel of air is heated, it expands and becomes less dense than the surrounding air. As a result, the parcel of air rises because it is less dense than the surrounding air, which creates a lower pressure area.
This process is known as convection and is responsible for many weather phenomena such as thunderstorms and cloud formation. In contrast, if a parcel of air cools and becomes more dense, it sinks because it creates a higher pressure area than the surrounding air.
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A sealed cylinder of length l and cross sectional area A contains n molecules of an gas at kelvin temperature T. What is the force acting on the cylinder marked A due to the gas?
A. NRT/l
B. NRT/lA
C. NkBT/lA
D. NkBT/l
I know it has to be option D but I have no idea how to get to that answer.
At kelvin temperature T, cylinder A includes n molecule of a gas, and the force exerted by the gas on the cylinder is NkBT/l.
Force is what?When two bodies interact, it refers to any form of pushing or pulling that one body exerts on the other. A vector quantity, that is. For instance, a person pushes or pulls on something to provide force, such as opening a door.
What variety of forces exist?Contact forces that act at a remove forces are the two different types of forces. Your daily use of force is evident. Basically, pressure and pull are forces.
Briefing:Formulas,
-P = F/A
-n = n/Na
-PV = nRT
= NKT (R = KNa)
- Volume of cylinder: A* l
F=PA
P = NKbT / V
P = NKbT / A* l
F = NkBT / A * l (A)
Cross out A,
Final, F = NkBT/l.
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What is the distance a catcher has to throw the ball from home to second base?
To throw out a runner, the catcher must toss the ball 130 feet out, 3 feet behind home plate, up to second base.
What is the explanation for the given answer?In order to throw out a runner, the catcher must throw the ball a distance of c=84.85 ft from home base to second base.
The distance between second base and the back tip of home plate shall be 127 feet, 3 inches.
As a result, although though the bases' "points" are 90 feet apart, the actual distance between each subsequent set of base markers is more like 88 feet (26.8 m).
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3. An air bubble of radius r rises steadily through
a liquid of density p at the rate of v. Neglecting
density of air, find the coefficient of viscosity of
liquid.
The coefficient of viscosity of a liquid can be determined from the motion of a bubble rising or falling through the liquid.
What is viscosity?
Viscosity basically is the measure of a fluid's resistance to flow. It is a measure of a fluid's internal friction, which is caused by the attraction of molecules in the fluid. Viscosity is an important physical property of fluids, as it affects the fluid's flow characteristics.
The equation for the coefficient of viscosity is given by:
2/9 r2 ρg/v.
where,
r = radius of bubble
ρ = density of liquid
g = acceleration due to gravity
v = velocity of bubble
Therefore, to calculate the coefficient of viscosity of a liquid, we need to know the radius of the bubble, the density of the liquid, the acceleration due to gravity, and the velocity of the bubble.
Hence, the coefficient of viscosity of liquid is 2/9 r2 ρg/v.
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If a building is 44 m tall, how long would it take to fall off it?
Answer:
2.995 seconds
Explanation:
We can use this kinematics equation to evaluate time.
[tex]y=v_0t-\frac{1}{2}gt^2[/tex]
Lets solve for [tex]t.[/tex]
Combine [tex]\frac{1}{2}[/tex] and [tex]gt^2[/tex].
[tex]y=v_0t-\frac{gt^2}{2}[/tex]
Subtract [tex]y[/tex] from both sides.
[tex]0=v_0t-\frac{gt^2}{2}-y[/tex]
[tex]0=-\frac{gt^2}{2} -v_0t-y[/tex]
Multiply both sides of the equation by -1.
[tex]0=\frac{gt^2}{2} -v_0t+y[/tex]
Multiply both sides of the equation by 2.
[tex]0=gt^2 -2v_0t+2y[/tex]
Use the quadratic formula to solve for t.
[tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
[tex]a=-g\\b=2v_0\\c=-2y[/tex]
Solution 1 Steps
[tex]t=\frac{-2v_0+\sqrt{(2v_0)^{2} -4*-g*-2y} }{2*-g}[/tex]
[tex]t=\frac{-2v_0+\sqrt{4v_0^2 -4*-g*-2y} }{2*-g}[/tex]
[tex]t=\frac{-2v_0+\sqrt{4v_0^2 -8gy} }{-2g}[/tex]
Solution 2 Steps
[tex]t=\frac{-2v_0-\sqrt{(2v_0)^{2} -4*-g*-2y} }{2*-g}[/tex]
[tex]t=\frac{-2v_0-\sqrt{4v_0^2 -4*-g*-2y} }{2*-g}[/tex]
[tex]t=\frac{-2v_0-\sqrt{4v_0^2 -8gy} }{-2g}[/tex]
One of these solution will most likely lead to a negative answer. The solution that gives a positive answer is correct. Lets enter our values into both equations to see which one is correct.
We can assume the initial velocity is 0.
We are given
[tex]v_0=0\\g=-9.81\\y=44[/tex]
Lets try the first solution.
[tex]t=\frac{-2*0+\sqrt{(4*0^2) -(8*-9.81*44)} }{-2*-9.81}[/tex]
[tex]t=\frac{0+\sqrt{0 -(8*-9.81*44)} }{-2*-9.81}[/tex]
[tex]t=\frac{0+\sqrt{0 --3453.12} }{-2*-9.81}[/tex]
[tex]t=\frac{\sqrt{3453.12} }{19.62}[/tex]
[tex]t=2.995[/tex]
Our first solution was positive so there is no need to check the second solution.
A 1 kilogram object is thrown horizontally and a 2 kilogram object is dropped vertically at the same instant and from the same point above the ground. If friction is neglected, at any given instant both objects will have the same
a) Total velocity
b) Momentum
c) Height
d) Kinetic energy
If friction is neglected, at any given instant both objects will have the same c) Height.
What is friction?
Friction is the resistance to motion that results from two objects rubbing against one another. Two objects rubbing against one another causes friction. Motion is opposed by friction, which works against the motion.
When an object slides over another object, friction slows it down. As a result, energy is used. However, the energy does not fade away. Kinetic energy, also referred to as moving energy, is transformed into heat energy. We rub our hands together when it's cold because of this. Rub them together, and friction and heat will result.
Learn more about friction
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