A ball is hit straight up

Question

A ball is hit straight up and reaches height of 295 feet. Neglecting air friction, what speed (mph) would the baseball attain if caught at same height it was hit.

Answer 1

Hi Elizabeth.

 

Questions asking about velocity at the end of a fall are most easily figured out by conservation of energy.

 

The potential energy at the bottom plus the kinetic energy at the bottom will equal the potential energy at the top plus the kinetic energy at the top.

 

KE_bot + PE_bot = KE_top + PE_top

 

There's no potential energy at the bottom of the fall, just as there's no kinetic energy at the top of the hit.

 

The potential energy at the top is mgh. The kinetic energy at the bottom is 1/2m*v².

 

So

 

mgh = 1/2*m*v²

 

gh = 1/2*v²

 

v = √(2gh)

 

= √(2*32*295)

 

= √(18880)

 

= 137.4 ft/sec

 

This is roughly 93 miles per hour, or the speed of a typical major league pitch. I'd consider stepping out of the way rather than trying to catch it.

 

Hope this helps.