Question

A tennis racket hits a tennis ball with a force of F=at−bt2, where a = 1200 N/ms , b = 370 N/ms2 , and t is the time (in milliseconds). The ball is in contact with the racket for 2.70 ms . If the tennis ball has a mass of 64.9 g , what is the resulting velocity of the ball, v, after the ball is hit by the racket? Express your answer numerically in meters per second to three significant fi

Answer 1

Given Information:  

Mass of tennis ball = m = 64.9 g

Contact time = Δt = 2.70 ms

Force = F = at - bt²

a = 1200 N/ms

b = 370 N/ms²

Assuming that a and b is given as newton per milliseconds

Required Information:  

Velocity of the ball = Vf = ?  

Answer:  

Vf = 22.496 m/s

Explanation:  

The change in momentum of the ball is given by

Δp = -FΔt

Lets first find out the force acting on the tennis ball

F = aΔt - bΔt²

F = (1200)(2.70) - (370)(2.70)²

F = 542.7 N

Δp =  542.7*0.0027

Δp = 1.46 N.s

Δp = mVf - mVi

initial velocity is zero

Vf = Δp/m

Vf = 1.46/0.0649

Vf = 22.496 m/s

Therefore, the speed of the ball is 22.496 m/s