# Q & A: speed of hit ball

Q:
When I kick a soccer ball, why does it always travel faster than the speed at which my foot kicked it? Same with tennis and baseball balls. For a tennis ball, the ball travels beyond 100 mph after I smashed it, but there's no way that I can swing my racquet at 100 mph!
- Anonymous
A:
You're right to see this as a pretty general behavior. Let's look at it in a simplified general way. Then you can make modifications for particular cases.

We'll use a deep fact- that we can choose whatever inertial reference frame we find convenient, and use the same simple laws of physics. Let's pick the reference frame in which your foot or racket or bat or whatever is at rest at the moment it and the ball hit each other. In that frame, if the ball was at rest with respect to the earth, the ball is rushing toward the foot at speed v, the same speed at which an earth-frame observer would say that the foot is moving. Let's make two simplifications: say that the collision is elastic and that the thing hitting the ball is much more massive than the ball. Then in the foot frame the ball just leaves the foot at speed v, just switching directions. Going back to the earth frame gives the ball's speed as 2v.

In real life the collisions aren't completely elastic and the mass of the foot etc. isn't infinite. So if the ball starts from rest, you expect it to leave at speed greater than about v but definitely less than 2v. If the ball is coming in at some speed (as in tennis volleys or baseball or some soccer kicks, that generally increases the speed out by increasing the total input energy, assuming that the foot etc. is a lot more massive than the ball.

Mike W.

(published on 07/23/2011)

## Follow-Up #1: How do you determine the speed of tennis ball?

Q:
How, and with what, is the ball speed determined in professional tennis matches?
- Graham (age 70+)
Victoria Australis
A:

Hi Graham,

With a radar gun, just like the cops use to catch speeders.   You send out a signal with a certain frequency and the returning echo is doppler shifted by an amount proportional to the relative speed between you and the ball.

LeeH

(published on 01/15/2014)