A tennis ball of mass 57. g bounces off a wall. Right before hitting the wall, the ball is moving to the right and up with vx=+40. m/s and vy=+10. m/s. Right after bouncing off the wall, the ball is moving to the left and up with vx=-35. m/s and vy=+10. m/s.

If the ball is in contact with the wall for 4.5 ms, what is the average force that the wall makes on the ball?

change of momentum normal to the wall

=m(vx1-vx0)=m(-35-40)=-75m kg-m/s
change of momentum parallel to wall
=m(vy1-vy0)=m(10-10) = 0 kg-m/s
Time = 4.5 ms
Average Force
= rate of change of momentum
= -75*0.057/(0.0045) N
= ?

To find the average force exerted by the wall on the ball, we need to apply Newton's second law of motion, which states that the force acting on an object is equal to the rate of change of momentum.

The momentum of an object can be calculated by multiplying its mass by its velocity. In this case, we have the velocities of the ball before and after the collision as well as its mass.

The initial momentum of the ball (P1) can be calculated by multiplying its mass (m) by its initial velocity (v1). P1 = m * v1

The final momentum of the ball (P2) can be calculated using its mass (m) and final velocity (v2). P2 = m * v2

The change in momentum (ΔP) can be calculated by subtracting the initial momentum from the final momentum. ΔP = P2 - P1

The average force (F) exerted by the wall on the ball can be calculated by dividing the change in momentum by the time during which the collision occurs. F = ΔP / Δt

In this case, we are given the mass of the ball (57 g = 0.057 kg), the initial velocities (vx = +40 m/s and vy = +10 m/s), the final velocities (vx = -35 m/s and vy = +10 m/s), and the collision time (4.5 ms = 0.0045 s).

Now, let's calculate the average force exerted by the wall on the ball step by step:

First, calculate the initial momentum (P1):
P1 = m * v1 = 0.057 kg * 40 m/s = 2.28 kg·m/s

Next, calculate the final momentum (P2):
P2 = m * v2 = 0.057 kg * (-35 m/s) = -1.995 kg·m/s

Then, calculate the change in momentum (ΔP):
ΔP = P2 - P1 = -1.995 kg·m/s - 2.28 kg·m/s = -4.275 kg·m/s

Finally, calculate the average force (F):
F = ΔP / Δt = -4.275 kg·m/s / 0.0045 s ≈ -950 N

Therefore, the average force exerted by the wall on the ball is approximately -950 Newtons. The negative sign indicates that the force is directed towards the left.