A tennis racket hits a tennis ball with a force of F=at-bt2, where a = 1290 N/ms, b = 330 N/ms2, and t is the time (in milliseconds). The ball is in contact with the racket for 2.80 ms. If the tennis ball has a mass of 55.6 g, what is the resulting velocity of the ball, v, after the ball is hit by the racket?

Question

Physics

Damion French

23 November, 13:29

A tennis racket hits a tennis ball with a force of F=at-bt2, where a = 1290 N/ms, b = 330 N/ms2, and t is the time (in milliseconds). The ball is in contact with the racket for 2.80 ms. If the tennis ball has a mass of 55.6 g, what is the resulting velocity of the ball, v, after the ball is hit by the racket?

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Kaia Boone · Answer 1

The resulting velocity of the ball after it hits the racket was of V = 51.6 m/s

Explanation:

m = 55.6 g = 0.0556 kg

t = 2.8 ms = 2.8 * 10⁻³ s

F = 1290 N/ms * t - 330 N/ms² * t²

F = 1024.8 N

F*t = m * V

V = F*t/m

V = 51.6 m/s