What is the average force exerted on the ball?

Question

a baseball of mass m and initial speed v strikes a catchers mitt, if the mitt moves a distance delta x as it brings the ball to rest, what is the average force exerted on the ball?

Answer 1

Use the law of conservation of energy.

Kinetic energy of ball = energy absorbed by catcher's mitt

KE of ball = (1/2)mv^2

Energy absorbed by catcher's mitt = F(delta x)

where

F = force exerted on mitt

delta x = distance at which mitt is moved during the catch

Equating the two,

(1/2)mv^2 = F(delta x)

and solving for "F",

F = mv^2/(2*delta x)