A baseball (m=145g) traveling 39 m/s moves a fielder's glove backward 23 cm when the ball is caught.
What was the average force exerted by the ball on the glove?
Express your answer to two significant figures and include the appropriate units.

The x-component of a vector are < 106.6, 43.07 >

Depending on the angle we are provided, the x-component of a vector can either be cos or sin. Cos always corresponds to the right triangle's side that contacts the specified angle.

If a vector v with magnitude ||v|| makes an angle θ with the positive x-axis then,

v = ||v|| cos θi + ||v|| sin θj

 =  < ||v|| cos θ , ||v|| sin θ >

Magnitude p = 115 km

Angle = 22°

p = ||p|| < cos θ, sin θ >

p = 115 < cos 22°, sin 22° >

p = 115 < 0.927, 0.3746 >

p = < 106.6, 43.07 >

Therefore,  the x-component of a vector are < 106.6, 43.07 >

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Infinity is the zero point for electric potential energy because Electric field strength is zero at infinity.

This conclusion is not "derived" from anything else; the electrostatic potential is zero at infinity because that is how we define it.

Define electric field and electric field strength.

The physical field that contains electrically charged particles and pulls or attracts all other charged particles in the vicinity is known as an electric field. Additionally, it describes the physical environment of a system of charged particles.

The intensity of an electric field at a specific location is expressed quantitatively as "electric field strength." The volt per meter (v/m or v m-1) is the common unit.

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(a) The number of turns of the coil is determined as 1,596 turns.

(b) The rate of change of current is determined as 1,130.43 A/s.

L = N²μA/l

where;

N²μA = LI

N² = LI/μA

N² = (2.3 x 10⁻³ x 2π x 0.062)/(4π x 10⁻⁷ x 2.8 x 10⁻⁴)

N² = 2,546,428.6

N = √2,546,428.6

N ≈ 1,596 turns

L = (emf)/I

I = (emf)/L

I = (2.6)/(2.3 x 10⁻³)

I = 1,130.43 A/s

Thus, the number of turns of the coil is determined as 1,596 turns.

The rate of change of current is determined as 1,130.43 A/s.

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The minimum work needed to pus the cart up the inclined plane is 960000 J.

The work done on a inclined plane is given below as:

Distance = 700 m

The force on an inclined plane, F = mgsinθ

where;

m is mass in kg

g = 9.81 m/s²

θ = 8.5°

Work done = 950 * 9.81 * sin 8.5 * 700

Work done = 960000 J

Therefore, minimum work needed is 960000 J.

In conclusion, the work done is a product of force and distance.

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Conduction is a process through which energy is transferred from the branding iron to the handle.

When two objects with different surface temperatures come into close touch with one another, conduction happens. Up until they reach thermal equilibrium, or the point at which they are at the same temperature, the heat energy moves from the hotter to the cooler object.

The metal tip of the branding iron, which makes contact with the branded surface, becomes extremely hot when it is placed in the fire because of the high fire temperature.

Hence, conduction is a process through which energy is transferred from the branding iron to the handle.

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(a) The magnitude of the minimum magnetic field is 1.467 T.

(b) The direction of the minimum magnetic field will be eastwards.

F = qvB

mg = qvB

B = mg/qv

where;

B = (1.98 x 10⁻⁴ x 9.8) / (3.5 x 10⁻⁸ x 3.78 x 10⁴)

B = 1.467 T

The magnetic field will be directed towards the negative charge. Thus, the direction of the minimum magnetic field will be eastwards.

Thus, the magnitude of the minimum magnetic field is 1.467 T and the direction is eastwards.

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The tension in the rope B is determined as 10.9 N.

tanθ = (6 - 4)/(5 - 0)

tan θ = (2)/(5)

tan θ = 0.4

θ = arc tan(0.4) = 21.8 ⁰

θ = 21.8 ⁰ + 21.8 ⁰ = 43.6⁰

Apply cosine rule to determine the tension in rope B;

A² = B² + C² - 2BC(cos A)

B = C

A² = B² + B² - (2B²)(cos A)

A² = 2B² - 2B²(cos 43.6)

A² = 0.55B²

B² = A²/0.55

B² = 65.3/0.55

B² = 118.73

B = √(118.73)

B = 10.9 N

Thus, the tension in the rope B is determined as 10.9 N.

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Hello!

This is an example of a force summation in the vertical direction.

We have the tension of rope A upward (+), and the equal vertical components of the tensions of rope B and C downward (-).

These forces sum to zero, since the knot is stationary.

[tex]\Sigma F = T_A - T_{By} - T_{Cy} \\\\0 = T_A - T_{By} - T_{Cy}[/tex]

Ropes 'B' and 'C' form equivalent angles from the vertical. (If you were to draw a line from rope A down). We can use right-triangle trig to determine the angle:

[tex]tan^{-1}(\frac{O}{A}) = \theta[/tex]

The ropes are 5 m long and 2 m tall, which are the opposite and adjacent sides respectively:
[tex]tan^{-1}(\frac{5}{2}) = 68.2^o[/tex]

The vertical components are the adjacent sides from this angle, so, we would use cosine.

[tex]0 = T_A - T_Bcos\theta - T_Ccos\theta[/tex]

Rope 'B' and 'C' have the same tensions since they form the same angle with the vertical and are the same length, so we can call them 'T'.

[tex]0 = T_A - 2Tcos\theta[/tex]

Solving for 'T':

[tex]2Tcos\theta = T_A \\\\T = \frac{T_A}{2cos\theta}\\\\T = \frac{65.3}{2cos(68.2)} = \boxed{87.92 N}[/tex]

The acceleration due to gravity near the surface of the planet is 27.38 m/s².

g = GM/R²

where;

g = (6.626 x 10⁻¹¹ x 2.81 x 5.97 x 10²⁴) / (6371 x 10³)²

g = 27.38 m/s²

Thus, the acceleration due to gravity near the surface of the planet is 27.38 m/s².

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I will go to school tomorrow .....is this present tense or past tense or future tense

Answer:

D

Explanation:

The given vector can be broken down into two components (as shown in the figure).

Which results ; vector (s) = 3x + 4y.

The image distance is 33.3 cm while the image height is 14.2 cm.

A converging lens will always have a positive focal length hence, we have to find the object distance as follows;

1/f = 1/v + 1/u

1/12 = 1/v + 1/20

1/v = 1/12 - 1/20

1/v = 0.08 - 0.05

v =33.3 cm

Now;

Magnification =  33.3 cm/20.0 cm =1.67

M = Image height/Object height

1.67 =  Image height/8.50 cm

Image height = 1.67  * 8.50 cm

Image height = 14.2 cm

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The weight of a 100-kg person decreases by 4 N when he goes from sea level to mountain top at an altitude of 5000 m.

The weight of a person is determined by the mass of the body and the acceleration due to gravity.

The acceleration due to gravity, g is dependent on the mass of the earth, M the radius of the earth and the gravitational force constant , G.

Mathematically, the acceleration due to gravity at the mountain top is determined using the formula:

where:

G = 6.67 × 10⁻¹¹ Nm²/kg²

M = 5.9736 x 10²⁴ kg

r = 638000 + 5000 = 6385000

g = (6.67 × 10⁻¹¹  *  5.9736 x 10²⁴ )(6385000)²

g = 9.77 m/s²

His weight at the mountain top will be:

weight = 100 * 9.77

weight = 977 N

Weight at sea level = 100 * 9.81 = 981 N

Decrease in weight = 981 - 977

Decrease in weight = 4 N

In conclusion, the weight of the man varies according to his distance from the earth.

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a. θ = 41. 4°

b. θ = 60°

c. θ = 75. 5°

d. θ = 90°

From the given information, we would be using the Malus' law

It is given as;

I = I0 cos²θ

Where I0 is the intensity of the polarized light after passing through P

a. To find the angle, compare with the given equation

I = (0.750)I0

I = I0 cos θ

then

cos θ = 0. 750

θ = [tex]cos^-^1(0. 750)[/tex]

θ = 41. 4°

b.  I = (0.500)I0

cos  θ = 0. 500

θ = [tex]cos^-^1(0. 500)[/tex]

θ = 60°

c.  I = (0.250)I0

cos θ = 0. 250

θ = [tex]cos^-^1 (0. 250)[/tex]

θ = 75. 5°

d.  I = 0

cos  θ = 0

θ = [tex]cos^-^1 (0)[/tex]

θ = 90°

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The actual weight of the stone is 11 N. It is based on the Archimedes principles.

Actual weight= weight inside water+ weight of water displaced

= 9N + 2N = 11N

Thus, we can conclude that the actual weight of the object is 11N.

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(a) The coil's self-inductance is 7.26 mH.

(b) The self-induced emf in the coil is 7.26 V

(c) The direction of the induced emf is from b to a.

L = N²μA/I

L = (600² x 4π x 10⁻⁷ x 6.9 x 10⁻⁴)/(0.043)

L = 7.26 x 10⁻³ H

L = 7.26 mH

emf = N(ΔBA)/t

where;

B = μNI/L

B1 = (4π x 10⁻⁷ x 600 x 5)/0.043

B1 = 0.0876 T

B2 =  (4π x 10⁻⁷ x 600 x 2)/0.043

B2 = 0.035 T

emf = NΔBA/t

emf = (600)(0.0876 - 0.035)(6.9 x 10⁻⁴) / (3 x 10⁻³)

emf = 7.26 V

The direction of the induced emf is always opposite to the direction of the applied current.

Thus, the direction of the induced emf is from b to a.

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vr>vs because the rolling ball acquires rotational as well as translational kinetic energy.

The accelerating force acting on the ball as it goes along a smooth plane is mgsin. Its acceleration is therefore equal to gsin. The mgsin acts down the plane as the ball travels down the rough inclined plane, but friction develops that acts up the plane.

Since both balls' potential energy is lost at the same rate, their KEs are actually equal at the base of the planes. However, a ball sliding down a smooth plane has only translational kinetic energy, but a ball rolling down a rough plane contains both translational and rotational kinetic energy at the bottom of the plane. As a result, the ball's translational KE will be lower than its translational Kinetic energy.

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The Force on the left hand pole, F' = 0.167N

Force is an agent which produces a change in the motion or state of an object.

Force is a vector quantity.

The general force is calculated as follows:

F = mg/sinθ

m = 17.1 g = 0.0171 kg

g = 9.81 m/s²

θ = 45°

F = 0.0171 * 9.81/sin45

F = 0.237 N

Force on the left hand pole, F' = Fcosθ

F' = 0.237 * cos 45

F' = 0.167N

In conclusion, the force on the left hand pole is the horizontal component of force.

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The altitude of the pole vaulter as she crosses the bar is 5 m.

v² = u² - 2gh

where;

h = (u² - v²)/2g

h = (10² - 1.5²)/(2 x 9.8)

h = 5 m

Thus, the altitude of the pole vaulter as she crosses the bar is 5 m.

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The volume that sticks out of the water is 83 m³.

To find the answer, we need to know about the archimedes principle.

= 1024 - 941 = 83 m³

Thus, we can conclude that the volume that sticks out of the water is 83 m³.

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With the use of below formula, at 879 °C,  velocity will be double the velocity at 15 °C.

The velocity of sound waves in air is proportional to the square root of Thermodynamic temperature. That is, V = K[tex]\sqrt{T}[/tex]

Given that the temperature at which the velocity of sound in air is twice its velocity at 15°C, Let us make use of the formula;

(v2/v1) = √(T2 / T1)

Where

Recall that absolute temperature = °C + 273.

If v2 = 2 × v1 and temperature in degree Celsius = 15°C, then,

Temperature in Kelvin K = 15 + 273 = 288

Substitute all the parameters into the formula

(2 × v1)/v1 = √(T2/288)

2 = √ (T2 /288)

Square both sides

4 = (T2/288)

T2 = 4 × 288

T2 = 1152K

Temperature in degrees Celsius = 1152 - 273 = 879 °C.

Therefore, at 879 °C,  velocity will be double the velocity at 15 °C.

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(a) The surface charge density in the sphere of radius 7.4 is 0.0322 C/m³.

(b) The surface density on the 2nd sphere is  3.48  x 10⁻⁴ C/m³.

F = kq₁q₂/r²

Fr² = kq₁q₂

q₁q₂ = Fr²/k

where;

q₁q₂ = (0.62 x 0.38²) / (9 x 10⁹)

q₁q₂ = 9.95 x 10⁻¹² C

q₂ = 9.95 x 10⁻¹² C/q₁

From the question;

q₁ + q₂ = 55 x 10⁻⁶

q₁ + 9.95 x 10⁻¹² /q₁ = 55 x 10⁻⁶

q₁² + 9.95 x 10⁻¹²  =  55 x 10⁻⁶q₁

q₁² - 55 x 10⁻⁶q₁  + 9.95 x 10⁻¹²   = 0

solve the quadratic equation using formula method;

q₁ = 5.48 x 10⁻⁵ C

q₂ = 55 x 10⁻⁶ C - 5.48 x 10⁻⁵ =  1.82 x 10⁻⁷ C

V1 = ⁴/₃πr³

V1 = (⁴/₃ π)(0.074)³ =  1.7 x 10⁻³ m³

Surface charge density = (5.48 x 10⁻⁵ C) / (1.7 x 10⁻³ m³) = 0.0322 C/m³

V2 = (⁴/₃ π)(0.05)³ = 5.236 x 10⁻⁴ m³

Surface charge density = ( 1.82 x 10⁻⁷ C) / (5.236 x 10⁻⁴ m³) = 3.48  x 10⁻⁴ C/m³

Thus, the surface charge density in the sphere of radius 7.4 is 0.0322 C/m³.

The surface density on the 2nd sphere is  3.48  x 10⁻⁴ C/m³.

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The net force is represented by ↓ 500N.

The net force is the force that has the same effect in magnitude and direction as two or more forces acting together.

Now we have the forces;

Thus we can obtain the net force as;

5500 N - 6000 N

= - 500 N

Therefore the net force is represented by ↓ 500N.

Missing parts:

Haley is trying to pull an object upward. The below forces are acting on the object.

Fp = 5500N

Fg = 6000N

Which represents the net force?

← 500N

→ 500N

↑ 500N

↓ 500N

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The height, h, of the water level in the tank is  mathematically given as

h=1.3675

Generally, the equation for kinematics is  mathematically given as

S=v_o t+(1/2)at^2

Therefore

y=0+(1/2)gt^2

Where

t=(2y/g)^{1/2}

t=(2*1.72/9.8)^{1/2}

t=0.5925s

The horizontal exit velocity will be given as

[tex]Vx=x/t[/tex]

Therefore

[tex]Vx=\frac{0.3.13}{0.5925}[/tex]

Vx=0.5283

In conclusion, applying Bernoulli's Law the tank bottom and tank surface

P+(1/2)pv0^2+pgh=P+(1/2)pvx^2+pgh

(1/2)(p)(0m/s)^2+pgh=(1/2)pvx^2+pg(0m)

gh=(1/2)vx^2

h=(0.5283m/s)^2/(2)(9.8)

h=1.3675

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The amount of work done to stop a 975- kg car traveling at 105 km/h is 414,808.34J.

The amount of work done by a moving object can be calculated using the following formula:

W (Kinetic energy) = ½ mv²

Where;

According to this question, a car of 975 kg is traveling at 105 km/h. This speed in m/s is 29.17m/s.

K.E = ½ × 975 × 29.17²

K.E = 414,808.34J

Therefore, the amount of work done to stop a 975- kg car traveling at 105 km/h is 414,808.34J.

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The steps of the use of the laser technique is explained below:

This refers to the type of surgery that makes use of special light beams in order to cut open the human body in a surgical procedure.

Hence, we can see that the laser technique is considered safer than conventional surgical methods.

Laser techniques include:

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The orbital speed of an ice cube in the rings of Saturn is determined as  355,366.5 m/s.

The orbital speed of an astronomical body or object is the speed at which it orbits around the center of mass of the most massive body.

The orbital speed of ice cube in the rings of Saturn is calculated as follows;

v = √GM/r

where;

v = √(6.67 x 10⁻¹¹ x 5.68 x 10²⁶)/(3 x 10⁵)

v = 355,366.5 m/s

Thus, the orbital speed of an ice cube in the rings of Saturn is determined as  355,366.5 m/s.

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From the calculations, the power developed is 337.5 W.

First we must obtain the acceleration from;

v = u + at

u = 0 m/s because the motion started rom rest

v = at

a = v/t

a = 12 m/s/ 1.6 s

a= 7.5 m/s^2

The force is obtained from;

F = ma = 7.5 kg * 7.5 m/s^2 = 56.25 N

Now the distance covered is obtained from';

v^2 = u^2 + 2as

v^2 = 2as

s = v^2/2a

s = (12)^2/2 *  7.5

s = 9.6 m

Now;

Work = Fs = 56.25 N *  9.6 m = 540 J

Power expended =  540 J/ 1.6 s = 337.5 W

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The restoring force on the spring is found to have exactly the same magnitude as the stretching force. Option D

The restoring force is the force that seeks to restore the spring to its equilibrium position. It has the same magnitude as the stretching force but acts in opposite direction.

Thus, the restoring force on the spring is found to have exactly the same magnitude as the stretching force.

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Answer:

The Gemini program

Explanation:

The Gemini Program was the second human spaceflight program hosted by Nasa in the year 1961. Taking place between mission Mercury and Apollo, the Gemini spacecraft carried two people to space and marked the foundation to the upcoming Apollo mission to Moon. It was a series of missions into the outer orbital which took place between 1965 and 1966. Prior to the Gemini missions, NASA had little to no information about space and space traveling. It was crucial for them to get acquainted with life outside before establishing successful Moon landings. And the series of Gemini missions helped them do just that.

A change in the linear speed of the Earth around the sun will cause a change in the magnitude of the centripetal acceleration.

Centripetal acceleration is the acceleration of a body moving a circular path.

The relationship between centripetal acceleration and speed;

a = v²/r

where;

Since the centripetal acceleration is directly proportional to square of linear speed, a change in the linear speed of the Earth around the sun will cause a change in the magnitude of the centripetal acceleration.

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In my opinion, I think that the input data that are required to find the least energy path are:

This refers to the use of a diagram to represent the features of a place that shows its physical landforms to help in navigation.

Hence, we can see that when using maps like gmaps, it is important to consider both elevation and distance to be able to find the path that uses the least energy.

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