How do I calculate the force applied to a tennis ball when it is hit by Pete?

[jrbillbrian]

Homework Statement

Pete serves a tennis ball of mass 54 grams at a speed of 53.6 meters per second. The ball is in contact with Pete's racket through a distance of 49.7 centimeters. What force does Pete apply to the ball?

54 grams = 0.054 kg
Speed = 53.6 m/s
49.7 cm = 0.0497 m

Homework Equations

Force = mass x acceleration
V_final = at + vi

The Attempt at a Solution

I am VERY lost, considering the fact that our teacher told us to try and figure it any way we could.

I tried this. 0.0497 m = 0.5(53.6 m/s) * t²
t = 0.0420183500 s

Then I thought of the statement
It takes 0.0420183500 seconds to travel 0.0497 m when traveling at 53.6 m/s

Then I tried V_final = a*t + V_initial
56.3 m/s = a * 0.0420183500 s

a = 1339.890784 m/s₂

Force = 0.054 kg * 1339.890784 m/s/s
Force = 72.4 N

Can anyone help me out with this please?

 

[JDHalfrack]

Since you are given the distance over which the force was applied, you should probably use an equation that has distance.

The way I read this question, you are given the following:
$$\Delta$$x = .497m
v_i = 0 (<-- not given, but I'm assuming the ball wasn't moving until he hit it)
v_f = 53.6 m/s

You are trying to find acceleration.

Find an equation that has $$\Delta$$x, v_i, v_f, and a in it, and solve for a.

Once you find acceleration, you can use the F = ma equation to find the force.

Does this make sense?

 

[jrbillbrian]

Yes, what you are suggesting seems to make sense. I will try it and let you know if I figure it out. Thanks

 

[jrbillbrian]

Thanks! I got it. One major and obvious problem that I discovered was the fact that I converted it to 0.0497 m rather than 0.497. I ended up using Vf^2 = Vi^2 + 2a * delta x
I solved for 156 Newtons. Thanks

 

[JDHalfrack]

I solved for 156 Newtons. Thanks

That's the same answer I got too. Good job! Glad to help!