Question

A racquet ball with mass m = 0.238 kg is moving toward the wall at v = 12.5 m/s and at an angle of θ = 31° with respect to the horizontal. The ball makes a perfectly elastic collision with the solid, frictionless wall and rebounds at the same angle with respect to the horizontal. The ball is in contact with the wall for t = 0.078 s.

a. What is the magnitude of the initial momentum of the racquet ball?

b. What is the magnitude of the change in momentum of the racquet ball?

c. What is the magnitude of the average force the wall exerts on the racquet ball?

d. Now the racquet ball is moving straight toward the wall at a velocity of vi = 12.5 m/s. The ball makes an inelastic collision with the solid wall and leaves the wall in the opposite direction at vf = -7.9 m/s. The ball exerts the same average force on the ball as before.
What is the magnitude of the change in momentum of the racquet ball?


e. What is the time the ball is in contact with the wall?

f. What is the change in kinetic energy of the racquet ball?

Answer 1

(a) magnitude of the initial momentum is
(0.238 kg)(12.5 m/s) = 2.975 kg*m/s.

(b) The horizontal component of the initial momentum is
(0.238 kg)(12.5 m/s)*cos(31) = 2.550 kg*m/s.
The change in momentum is -2*2.550 kg*m/s, so the magnitude of the change is 5.10 kg*m/s.

(c) average F = delta-p/delta-t
= (5.10 kg*m/s)/(0.078 s) = 65.4 N.

(d) |delta-p| = (20.4 m/s)*(0.238 kg)
= 4.855 kg*m/s.

(e) t = (4.855 kg*m/s)/(65.4 N) = 0.0742 s.

(f) Change in KE is
(1/2)(0.238 kg)[(7.9 m/s)^2 - (12.5 m/s)^2]
= -11.17 J