skier accelerates down the hill at a speed of 18 and reaches the bottom of the hill at a speed of 36 in 6 seconds
What an acceleration of the skier​

Answer:

b.

Explanation:

Answer:

Attractive force and r = 0.399 m

Explanation:

One charge is positive and the other charge is negative. Opposite charges attract, so there has to be a force that attracts between them.

q1 = 10.0 x 10^-6 C

q2 = -3 x 10^-6 C

F = 1.7 N

Plug those values into Coulomb's Law:

[tex]F = k\frac{q1q2}{r^{2} } \\1.7 = \frac{(9x10^{9})(10.0 x 10^{-6})(-3 x 10^{-6})}{r^{2} }[/tex]

Solve for r

r = 0.399 m

Answer:

1st: Radiation

2nd: Conduction

3rd: Convection

Explanation:

I actually learned this before in school. Yay

Answer:

1. sand and water

2. suspension

mark me as brainliest plz

Answer:

I think its A

Explanation:

Not 100 percent sure tho but they do go up and down in big movements.

Answer:

d = 1.07 mile

Explanation:

The rationale for this method is that the speed of light is much greater than the speed of sound, the definition of speed in uniform motion is  

v = d / t  

d = v t  

the speed of sound is worth  

v = 343 m / s  

Therefore, the speed of sound must be multiplied by time to do this, all the units must be in the same system, as the distance in miles is requested  

v = 343 m/s (1mile/1609 m) (3600s/1 h) = 343 (2.24) = 767.4 mile/h  

v = 343 m / s (1 mile / 1609 m) = 0.213, mile/ s  

If the measured time is t = 5s we multiply it by the speed  

we substitute  

d = 0.213 5

d = 1.07 mile

If you want to calculate the speed, this method in general is not widely used, since you must know the distance where the lightning occurred, which is relatively complicated.

The image distance from the converging lens is 10.2 cm.

The focal length of the converging lens, f = 28 cm

The distance of the object from the converging lens, u = -16 cm

The optical center or axis of a convergent lens serves as the focal point for light, a lens that generates a real image by converting parallel light beams to convergent light rays.

The image is real and inverted so long as the item is not in the center of the lens.

According to the lens formula,

1/v + 1/u = 1/f

1/v = 1/f - 1/u

1/v = 1/28 - 1/-16

1/v = 1/28 + 1/16

1/v = 44/448

Therefore, the image distance from the converging lens is,

v = 448/44

v = 10.2 cm

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The train covers a distance of 100 meters in the given time.

To find the distance covered by the train in the given time, we can use the equations of motion.

S = ut + (1/2)at²

The equation S = ut + (1/2)at² is derived from the basic equations of motion. The first term (ut) represents the distance covered in the initial velocity u multiplied by time t. The second term (1/2)at² represents the distance covered due to the acceleration a during time t.

The initial velocity (u) of the train is 10 m/s, and the acceleration (a) is 4 m/s². We are given that this acceleration is attained after 5 seconds, so the time (t) is also 5 seconds. We need to find the distance covered (S).

Substituting the given values:

S = (10 m/s)(5 s) + (1/2)(4 m/s²)(5 s)²

S = 50 m + (1/2)(4 m/s²)(25 s²)

S = 50 m + 50 m

S = 100 m

It's important to note that the given problem assumes a constant acceleration throughout the entire time interval.

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The decrease in wave speed in layer B can be explained by the change in the properties of the medium through which the wave is propagating. Generally, the speed of a wave depends on the properties of the medium it is traveling through, such as the density and elasticity.

There are several factors that can lead to a decrease in wave speed in layer B:

Change in Density: If the density of the medium increases in layer B compared to layer A, it will result in a decrease in wave speed. This is because a denser medium tends to slow down the propagation of waves.

Change in Elasticity: If the elasticity (or stiffness) of the medium decreases in layer B compared to layer A, it can cause a decrease in wave speed. A less elastic medium offers more resistance to wave propagation, resulting in slower wave speed.

Change in Temperature: In some cases, temperature variations can affect the properties of the medium. For example, in the case of sound waves, as temperature increases, the speed of sound generally increases due to an increase in the elasticity and average kinetic energy of the molecules. Conversely, a decrease in temperature can lower the wave speed.

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The block's speed after it has traveled 2.0 m up the inclined plane, ignoring friction, is approximately 6.19 m/s.

To determine the block's speed after it has traveled 2.0 m up the inclined plane, we can use the principles of kinematics. We'll consider the initial speed, distance traveled, and the angle of the inclined plane.

Using the kinematic equation:

v^2 = u^2 + 2as

where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.

Given that the initial speed (u) is 8.0 m/s and the distance traveled (s) is 2.0 m, we need to find the acceleration (a).

The component of gravity acting down the inclined plane is given by:

mg sin(θ)

where m is the mass of the block and θ is the angle of the inclined plane.

Since there is no friction, the net force along the incline is equal to the component of gravity acting down the incline:

ma = mg sin(θ)

Canceling out the mass (m) on both sides:

a = g sin(θ)

Using the known values of the angle of the inclined plane (θ = 32°) and the acceleration due to gravity (g = 9.8 m/s^2):

a = (9.8 m/s^2) sin(32°)

a ≈ 5.27 m/s^2

Now we can substitute the values into the kinematic equation:

v^2 = u^2 + 2as

v^2 = (8.0 m/s)^2 + 2(5.27 m/s^2)(2.0 m)

v^2 ≈ 64.0 m^2/s^2 + 21.08 m^2/s^2

v^2 ≈ 85.08 m^2/s^2

Taking the square root of both sides:

v ≈ √(85.08 m^2/s^2)

v ≈ 9.23 m/s

Therefore, the block's speed after it has traveled 2.0 m up the inclined plane, ignoring friction, is approximately 9.23 m/s.

The block's speed after it has traveled 2.0 m up the inclined plane, ignoring friction, is approximately 9.23 m/s. This calculation is based on the initial speed, distance traveled, and the angle of the inclined plane, using principles of kinematics.

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The value of the load resistor (R) is approximately 7.47 Ω. The internal resistance of the battery is approximately 2.64 Ω.

To determine the value of the load resistor (R) and the internal resistance of the battery, we can use Ohm's law and the power formula. Let's break down the calculations for each part:

(a) Finding the value of R:

The power (P) delivered to the load resistor can be calculated using the formula P = V²/R, where V is the voltage and R is the resistance. Given that the power delivered is 24.0 W and the voltage is 13.4 V, we can rearrange the formula to solve for R:

R = V²/P = (13.4 V)² / 24.0 W ≈ 7.47 Ω.

(b) Determining the internal resistance of the battery:

The total voltage (V_total) across the battery can be calculated by adding the voltage drop across the load resistor (V_load) to the voltage drop across the internal resistance of the battery (V_internal).

We know that V_total = V_load + V_internal = 13.4 V.

Since V_load = IR (Ohm's law), where I is the current flowing through the circuit, we can substitute I = P/V_load = 24.0 W / 13.4 V.

Substituting these values into the equation, we have 13.4 V = (24.0 W / 13.4 V)R + V_internal.

To solve for V_internal, we rearrange the equation as follows:

V_internal = 13.4 V - (24.0 W / 13.4 V)R.

Substituting the values of V, P, and R, we find:

V_internal ≈ 13.4 V - (24.0 W / 13.4 V)(7.47 Ω) ≈ 2.64 Ω.

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(a) The magnitude of the impulse experienced by the soccer ball during the bounce is 0.6923 kg·m/s, (b) the magnitude of the constant force acting on the soccer ball during the bounce is 13.846 N and (c) the soccer ball transferred approximately 12.026 joules of energy to the environment during the bounce.

What is energy and how is it measured?

Energy is a fundamental concept in physics that refers to the ability of a system to do work or cause a change. It is a scalar quantity and is associated with various forms, such as kinetic energy, potential energy, thermal energy, and others.

The SI unit of energy is the joule (J).

Part (a):

The magnitude of the impulse (J) experienced by the soccer ball during the bounce can be calculated using the equation:

J = Δp,

where Δp is the change in momentum.

The change in momentum is given by:

Δp = m * Δv,

where m is the mass of the soccer ball and Δv is the change in velocity.

The initial velocity of the soccer ball is zero as it is dropped from rest. The final velocity can be calculated using the equation for final velocity in free fall:

v² = u² + 2gh,

where v is the final velocity, u is the initial velocity (zero in this case), g is the acceleration due to gravity, and h is the height.

Calculating the final velocity:

v²  = 0² + 2 * 9.8 m/s² * 2.12 m,

v ≈ 6.02 m/s.

Substituting the values into the equation for change in momentum:

Δp = m * (v - u),

Δp = 0.115 kg * (6.02 m/s - 0 m/s).

Calculating:

Δp ≈ 0.6923 kg·m/s.

Therefore, the magnitude of the impulse experienced by the soccer ball during the bounce is approximately 0.6923 kg·m/s.

Part (b):

The magnitude of the constant force (F) acting on the soccer ball can be calculated using the equation:

F = Δp / Δt,

where Δp is the change in momentum and Δt is the time interval.

Given that the soccer ball was in contact with the ground for Δt = 0.05 s, we can substitute the values into the equation:

F = 0.6923 kg·m/s / 0.05 s.

Calculating:

F = 13.846 N.

Therefore, the magnitude of the constant force acting on the soccer ball during the bounce is 13.846 N.

Part (c):

The energy transferred to the environment during the bounce can be calculated as the work done by the force of the ball on the ground.

The work done is given by:

W = F * d,

where F is the magnitude of the force and d is the distance over which the force acts.

In this case, the force acts over the distance between the initial and final heights, which is h₁ - h₂.

Substituting the values:

W = 13.846 N * (3.05 m - 2.12 m).

Calculating:

W ≈ 12.026 J.

Therefore, the soccer ball transferred approximately 12.026 joules of energy to the environment during the bounce.

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Answer:

since the charges are of different nature it's a attractive force

Explanation:

magnitude of force=

9*10^9*5*10^-6*3*10^-6/0.04

= 3.375N answer

The q3q3 is located at approximately x = -0.119 m on the x-axis. when the net force on q1q1 is 7.00 N.

Given:

Charge q1 = +3.00 μC at the origin (x = 0 m).

Charge q2 = -5.00 μC at x = 0.200 mm = 0.0002 m.

Charge q3 = -8.00 μC (location unknown).

We need to determine the location of q3 such that the net force on q1 is 7.00 N in the -x direction.

The force between two charges can be calculated using Coulomb's law:

F = k * |q1 * q2| / r^2

Where:

F is the force between the charges.

k is Coulomb's constant, approximately 8.99 × 10^9 N m^2/C^2.

|q1| and |q2| are the magnitudes of the charges.

r is the distance between the charges.

Let's first calculate the force between q1 and q2. Since q1 and q2 have opposite charges, the force will be attractive:

F12 = k * |q1 * q2| / r12^2

Substituting the given values:

F12 = (8.99 × 10^9 N m^2/C^2) * |3.00 × 10^-6 C| * |-5.00 × 10^-6 C| / (0.0002 m)^2

F12 = -0.67425 N

The negative sign indicates that the force is in the -x direction.

Now, let's consider the force between q1 and q3. The net force on q1 is given as 7.00 N in the -x direction. Therefore, the force between q1 and q3 should be:

F13 = -7.00 N - F12

Substituting the values:

-7.00 N = -7.00 N - (-0.67425 N)

-7.00 N = -7.00 N + 0.67425 N

-7.00 N = -6.32575 N

The force between q1 and q3 is approximately -6.32575 N.

We can calculate the distance between q1 and q3 using the formula for force:

F13 = k * |q1 * q3| / r13^2

Substituting the known values:

-6.32575 N = (8.99 × 10^9 N m^2/C^2) * |3.00 × 10^-6 C| * |-8.00 × 10^-6 C| / r13^2

Simplifying the equation:

r13^2 = (8.99 × 10^9 N m^2/C^2) * |3.00 × 10^-6 C| * |-8.00 × 10^-6 C| / -6.32575 N

r13^2 = 0.4048 m^2

Taking the square root of both sides:

r13 = √0.4048 m^2

r13 ≈ 0.6367 m

The distance between q1 and q3 is approximately 0.6367 m.

Since q3 has a negative charge and the net force on q1 is in the -x direction, q3 must be located to the left of q1. Therefore, the position of q3 is approximately x = -0.6367 m.

The q3q3 is located at approximately x = -0.119 m when the net force on q1q1 is 7.00 N.

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For an otto cycle:

a) Highest temperature and pressure are 1000K and 2.5 MPa.

b) amount of heat transferred, 150.2 kJ/kg

c) thermal efficiency, 56.5%

d) mean effective pressure is 1.31 MPa.

Given:

Initial conditions T1 = 27C = 300K, P1 = 100 kPa = 100 × 10³ Pa, V1 = 500 cm³ = 500 × 10⁻⁶ m³

Compression ratio (r) = V1/V2 = 10

End of isentropic expansion T3 = 1000 K

Specific heat ratio (k) = 1.4

Specific heat at constant pressure (cp) = 1.005 kJ/kg.K = 1005 J/kg.K

Specific heat at constant volume (cv) = 0.718 kJ/kg.K = 718 J/kg.K

Gas constant (R) = 0.287 kJ/kg.K = 287 J/kg.K

a) Highest temperature and pressure in the cycle:

At the end of the isentropic compression (point 2), we use the relation T2 = T1 × (V1/V2)^(k-1)

⇒ T2 = 300 K × 10^(1.4-1) = 300 K × 10^0.4 = 509 K

The pressure at the end of the compression stroke (point 2) is given by P2 = P1 × (V1/V2)^k

⇒ P2 = 100 × 10³ Pa × 10^1.4 = 2.5 MPa

The maximum temperature T3 is given in the problem as 1000K.

The maximum pressure in the cycle is the pressure at point 2, P2 = 2.5 MPa.

b) Amount of heat transferred:

The heat input is during the constant volume process 2-3, given by Q_in = m × cv × (T3 - T2)

But we do not have the mass (m) of the gas, we can calculate the change in internal energy per unit mass as ΔU = cv × (T3 - T2) = 718 J/kg.K × (1000K - 509K) = 352.6 kJ/kg

The heat rejected is during the constant volume process 4-1, given by Q_out = m × cv × (T4 - T1)

Using the adiabatic process, we know that T4 = T1 × (V2/V1)^(k-1) = 300 K × 10^0.4 = 509 K

ΔU = cv × (T4 - T1) = 718 J/kg.K × (509K - 300K) = 150.2 kJ/kg

c) Thermal efficiency:

The thermal efficiency of an Otto cycle is given by η = 1 - 1/(r^(k-1))

⇒ η = 1 - 1/(10^0.4) = 0.565 or 56.5%

d) Mean effective pressure (mep):

The thermal efficiency can also be expressed as η = 1 - V2/V1 = mep/(P2 - P1)

⇒ mep = η × (P2 - P1) = 0.565 × (2.5 MPa - 100 kPa) = 1.31 MPa

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Complete question:

An Otto cycle with compression ratio of 10.The air is at 100 kPa,27C,and 500 cm prior to the compression stroke. Temperature at the end of isentropic expansion is 1000 K. Determine the followings

a) Highest temperature and pressure in the cycle b) amount of heat transferred, c) thermal efficiency, and d) mean effective pressure. Use constant specific heat approach - k=1.4, cp= 1.005 kJ/kg.K cv= 0.718 kJ/kg.K, R = 0.287 kJ/kg.K 10 points

Answer:

B

Explanation:

The magnetic field strength needed on the square loop to create a maximum torque of 320 N·m is approximately 43.24 N/A.

To calculate the magnetic field strength needed to create a maximum torque on a square loop, we can use the formula:

Torque (T) = N × B × A × sinθ

Where:

T = Torque

N = Number of turns in the loop

B = Magnetic field strength

A = Area of the loop

θ = Angle between the magnetic field and the plane of the loop

In this case, we are given:

N = 185 turns

A = (20.0 cm)² = 0.04 m² (since the loop is square)

T = 320 N·m

θ = 90 degrees (since the torque is maximum)

Rearranging the formula, we can solve for B:

B = T / (N × A × sinθ)

Substituting the given values:

B = 320 N·m / (185 × 0.04 m² × sin(90°))

B = 320 N·m / (7.4 m²)

B ≈ 43.24 N/A

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The question is -

Calculate the magnetic field strength needed on a 185-turn square loop 20.0 cm on a side to create a maximum torque of 320 N·m, if the loop is carrying 21 A.

T?

The volume of water in the 250 mL cylinder is approximately 249.975 mL.

To calculate the volume of water, we multiply the density of water by the volume of the cylinder.

Given:

Density of water = 0.9999 g/mL

Volume of the cylinder = 250 mL

The formula for calculating the volume of a substance is:

Volume = Mass / Density

Since we are given the density and we want to find the volume, we rearrange the formula as:

Volume = Mass / Density

The mass can be obtained by multiplying the density by the volume:

Mass = Density * Volume

Substituting the given values:

Mass = 0.9999 g/mL * 250 mL

Simplifying, we get:

Mass = 249.975 g

Therefore, the volume of water in the 250 mL cylinder is approximately 249.975 mL.

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The voltage of the generator in the series RCL circuit at resonance is approximately 122.64 volts.

To determine the voltage of the generator in a series RCL circuit, we need to use the power and current values. In a series RCL circuit at resonance, the power dissipated is equal to the power supplied by the generator.

In this case:

Power dissipated (P) = 65.0 W

Current (I) = 0.530 A

The formula for power in an electrical circuit is:

P = VI

Where:

P is the power in watts

V is the voltage in volts

I is the current in amperes

Rearranging the formula to solve for voltage (V), we get:

V = P / I

Substituting the given values:

V = 65.0 W / 0.530 A

V ≈ 122.64 volts

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Answer:

[tex]55.64\ \text{nm}[/tex]

Explanation:

[tex]\lambda[/tex] = Wavelength falling on film = 520 nm

n = Refractive index of film = 2.62

T = Thickness of film

m = Order

We have the relation

[tex]2T=\dfrac{m\lambda}{n}\\\Rightarrow T=\dfrac{m\lambda}{2n}\\\Rightarrow T=\dfrac{m\times 520}{2\times 2.62}\\\Rightarrow T=99.24m[/tex]

The thickness should be greater than 1036 nm. This means [tex]m=11[/tex]

[tex]T=99.24\times 11=1091.64\ \text{nm}[/tex]

Thickness of the film to be added would be

[tex]\Delta T=1091.64-1036=55.64\ \text{nm}[/tex]

Thickness of the film to be added is [tex]55.64\ \text{nm}[/tex].

Answer:

Explanation:

The ray of light is passing from high refractive index medium to low refractive index medium so condition for cancellation of reflected light is as follows .

2μt = (2n+1) λ/2

where μ is refractive index of the medium , t is thickness , λ is wavelength of light and n is a integer .

Putting n = 10

2x 2.62 x t = 21 x 520 / 2 nm

5.24 t = 5460 nm

t = 1042 nm

Thickness required to be added

= 1042 - 1036 = 6 nm .

The force F2 will produce a torque about an axis perpendicular to the plane of the diagram at the left end of the rod.

To determine which force produces a torque about an axis perpendicular to the plane of the diagram at the left end of the rod, we need to consider the concept of torque and the position of the forces relative to the axis.

Torque is the rotational equivalent of force and is given by the equation: Torque = Force × Distance × sin(θ), where Force is the magnitude of the force, Distance is the perpendicular distance from the axis of rotation to the line of action of the force, and θ is the angle between the force and the lever arm.

In the given diagram, we have two forces acting on the rod, F1 and F2. The lever arm for each force is the distance from the left end of the rod to the line of action of the force.

For force, F1, the line of action passes through the left end of the rod. Therefore, the lever arm is zero, and sin(θ) is also zero since the angle between the force and the lever arm is 0 degrees. Consequently, the torque produced by force F1 is zero.

For force, F2, the line of action is not passing through the left end of the rod. The lever arm for force F2 is the perpendicular distance from the left end of the rod to the line of action of F2. Since this distance is non-zero and the angle between the force and the lever arm is non-zero, both the distance and sin(θ) are non-zero.

Therefore, the torque produced by force F2 is non-zero and will produce a torque about an axis perpendicular to the plane of the diagram at the left end of the rod.

Out of the two forces pictured, the only force F2 will produce a torque about an axis perpendicular to the plane of the diagram at the left end of the rod. Force F1 will not produce any torque since its line of action passes through the left end of the rod, resulting in a lever arm of zero.

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Answer: The resistance in the circuit is 250 ohms

Explanation:

According to Ohm's law:

[tex]V=IR[/tex]

where V = voltage  = 55 V

I = current in Amperes = 0.22 A

R = Resistance = ?

Putting in the values we get:

[tex]55V=0.22A\times R[/tex]

[tex]R=250ohm[/tex]

Thus the resistance in the circuit is 250 ohms

Answer:

The body systems that work together to maintain the energy Sierra needs are;

The digestive system, the respiratory system, and the circulatory system

Explanation:

Cellular respiration in the body cells require oxygen to produce energy which are used by the muscles and other body cells. Carbon dioxide is also produced and is the build up of carbon dioxide has to be removed from the body as the by product of cellular respiration which is toxic at the cell level

Therefore, the body systems that work together to maintain the energy Sierra needs are;

The digestive system; Takes in the energy containing food and brakes them into chemicals that are transported to the cells for cellular respiration

The respiratory system; Takes in oxygen and removes carbon dioxide from the blood from and to the atmosphere

The circulatory system; Supplies food and oxygen from the digestive and respiratory system to the cells and transports produced carbon dioxide from the cells to the lungs from where it is passed out of the body by th respiratory system.

The potential difference across the 2 Ω resistor is 2 V.

The potential difference across the 2 Ω resistor is equal to the current flowing through it multiplied by the resistance of the resistor. The current flowing through the circuit is 1 A, and the resistance of the 2 Ω resistor is 2 Ω.

Therefore, the potential difference across the 2 Ω resistor is:

= 1 A * 2 Ω = 2 V.

V = I * R

V = 1 A * 2 Ω

V = 2 V

Therefore, the potential difference across the 2 Ω resistor is 2 V.

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The angle at which the second-order maximum is produced in the diffraction grating is 36.97°.

Angle at which the first-order maximum is produced, θ₁ = 17.5°

The equation for the diffraction grating is given by,

nλ = 2d sinθ

Given that the same light is used for both diffraction grating procedures. The equation for wavelength can be given as,

λ = 2d sinθ/n

So, we can say that,

λ₁ = λ₂

2d sinθ₁/n₁ = 2d sinθ₂/n₂

sinθ₁/n₁ = sinθ₂/n₂

So,

sinθ₂ = n₂sinθ₁/n₁

sinθ₂ = 2 x sin(17.5)/1

sinθ₂ = 2 x 0.30071

sinθ₂ = 0.60142

Therefore, the angle at which the second-order maximum is produced is given by,

θ₂ = sin⁻¹(0.60142)

θ₂ = 36.97°

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Option (A) because a force acts on it , is the correct option .

A space probe in remote outer space continues moving because a force acts on it.

According to Newton's first law of motion, an object will continue to move in a straight line at a constant velocity unless acted upon by an external force. In the case of a space probe in remote outer space, several forces can act on it to maintain its motion.

One of the significant forces at play is gravity. While space is mostly empty, gravitational forces from celestial bodies can still influence the probe's trajectory. If the probe is near a massive object like a planet or a star, the gravitational force exerted by that object can provide the necessary force to keep the probe moving. In this scenario, the probe would move in a curved path around the massive object due to the gravitational force acting as a centripetal force.

Additionally, other forces such as propulsion systems, solar radiation pressure, or gravitational assists from planetary flybys can also act on the space probe, ensuring its continued motion and trajectory adjustments.

A space probe in remote outer space continues moving due to the presence of external forces acting on it. These forces, such as gravity, propulsion systems, solar radiation pressure, or gravitational assists, provide the necessary force to counteract any potential deceleration or deviation from its intended path.

While the probe may move in a curved path due to gravitational forces, it ultimately remains in motion because forces act upon it. Therefore, option A) is the correct choice.

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Solution :

As the charge is stationary, hence

[tex]$F_m= qvB \sin \theta$[/tex]

[tex]$F_m=0$[/tex]

Hence, no torque at all.

When the charge is moving in positive x direction and the field will be in the negative y direction outside the bar, then :

[tex]$F = q(V \hat i \times B(- \hat j))$[/tex]

    [tex]$= -qV B (\hat i \times \hat j)$[/tex]

    [tex]$=qVB(- \hat k)$[/tex]

Hence, the force have direction [tex]$(- \hat k)$[/tex].

When instead of charge, an iron nail is used, then there will be induced magnetic field in the soft iron. The nature of the pole induced will be opposite near tot he bar. That is the north pole will be induced near the south pole and vice versa. That is why whichever be the pole of magnet closest to iron will be attracted by iron.

We are givenInitial velocity vector vA has a magnitude of 3.00 meters per second and points 20.0o north of east, while final velocity vector vB has a magnitude of 6.00 meters per second and points 40.0o south of east. We need to find the magnitude and the direction of the change in velocity vector Δv (which is the vector subtraction of the two vectors:

final velocity vector minus initial velocity vector).Let's solve the given problem:From the above figure, the direction of Δv is at an angle θ to the east of south:

[tex]θ = θ2 - θ1= 40.0 - (-20.0)= 60.0o[/tex]

Magnitude of the Δv: Let's use the Pythagorean theorem to find the magnitude of Δv. We have:[tex]$$|\Delta \vec{v}| = \sqrt{|\vec{v}_B|^2+|\vec{v}_A|^2-2|\vec{v}_A||\vec{v}_B|\cos(\theta)}$$[/tex]  

Putting the given values in the above equation, we get

[tex]$$|\Delta \vec{v}| = \sqrt{(6.00)^2+(3.00)^2-2(6.00)(3.00)\cos(60.0)}$$$$|\Delta \vec{v}| = 3.10\ \text{m/s}$$[/tex]

So, the magnitude of the Δv is 3.10 m/s.Therefore, the magnitude and the direction of the change in velocity vector Δv is 3.10 m/s at an angle of 60.0o to the east of south.

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