Question

When a tennis ball is hit by a racquet, the racquet strings and ball distort, providing a restoring force much like a spring. Thus the collision is approximately elastic.Regulation tennis balls have a mass of approximately 0.06 kg, and modern racquets have a mass of approximately 0.6 kg and are about 70 cm long.

THIS IS A SENARIO THAT WILL BE ON MY FINAL. I NEED HELP WITH POSSIBLE QUESTIONS THAT COULD BE ASKED, AND EQUATIONS TO GO WITH THOSE. PLEASE AND THANKS!

Answer #1

One example is

Q- A tennis ball of mass 0.022 kg is moving at 3.1 m/s at an
angle of 222° to the horizontal. It is struck by a racket which
exerts a force on it of 72t - 442 t^2 N for 1/10 of a second at an
angle 32° to the horizontal. Find the final velocity of the tennis
ball (Express answer using i and j unit vectors)

Ans:

p = mv (momentum)

Δp = pf - pi

1.- Integrate the force exerted by racket, using tf = 0.1 s and ti = 0

Δp = ∫ F dt = 0.218 Km m / s

2.- Divide Δp in x and y components, by multiplying 0.218 by cos 222° and sin 222°, respectively.

3.- Obtain ball's momentum, in components also:

px initial = (0.022 kg)(3.1 m/s) cos 32°

py initial = (0.022 kg)(3.1 m/s) sin 32°

4.- Using Δp = pfinal - pinitial, solve for pfinal, which is (mass)(vel. final), then solve for vel. final.

v final = (Δp + p initial) / mass = (6.05 i + 3.2 j) m/s

Hope this helps

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