One billiard ball is shot east at 3.0 m/s. A second, identical billiard ball is

Question

One billiard ball is shot east at 3.0 m/s. A second, identical billiard ball is shot west at 1.0 m/s. The balls have a glancing collision, not a head-on collision, deflecting the second ball by 90° and sending it north at 1.44 m/s. What are the speed and direction of the first ball after the collision? Give the direction as an angle south of east.

A tennis player swings her 1000 g racket with a speed of 12 m/s. She hits a 60 g tennis ball that was approaching her at a speed of 23 m/s. The ball rebounds at 41 m/s.

(a) How fast is her racket moving immediately after the impact? You can ignore the interaction of the racket with her hand for the brief duration of the collision.
   m/s

(b) If the tennis ball and racket are in contact for 10 ms, what is the average force that the racket exerts on the ball?
N

How does this compare to the gravitational force on the ball?

Explanation / Answer

Momentum is conserved for each directional component.

west-east direction:
(m)(3 m/s) + (m)(-1m/s) = (m)(vx) + 0
3 - 1 = vx
vx = 2 m/s (moving east)

north-south direction:
0 = (m)(vy) + (m)(1.44 m/s)
vy = -1.44 m/s (moving south)

v = sqrt[(vx)² + (vy)²]
v = sqrt[(2)² + (-1.44)²]
v = 2.46 m/s

tan = -1.44 / 2 (in Quad IV)
= -35.75° (35.75° south of east)

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