Question

During the 2007 French Open, Venus Williams hit the fastest recorded serve in a premier women’s match, reaching a speed of 58 m/s (209 km/h).

What is the average force exerted on the 0.057-kg tennis ball by Venus Williams’ racquet, assuming that the ball’s speed just after impact is 58 m/s, that the initial horizontal component of the velocity before impact is negligible, and that the ball remained in contact with the racquet for 5.0 ms (milliseconds)?


a)660 N

b)1660 N

c)25 N

d)4000 N

Answer 1

a) 660 N

Step-by-step explanation:

We know that:

FΔt = ΔP

Where F is the force, Δt is the time in contact and ΔP is the change in the linear momentum.

First, we will change the contact time form milliseconds to seconds

t = 5.0 ms = 0,005 s

Second we will find the change of the linear momentum:

ΔP =
`P_f -P_i`

so:

`P_i = MV_i\\P_f = MV_f`

Where M is the mass of the ball, Vi is the velocity before the impact and Vf is the velocity after the impact.

The ball don't have horizontal velocity before impact so, it don't have momentum.

Replacing and solving for F, we get:

FΔt= M
`V_f`

F(0.005) = 0.057(58 m/s)

F = 661.2 N