a kid with a baseball cap is playing catch with himself by trowing a ball straight up how fastdoes he throw the ball if it comes back to his cap in0.8 seconds later

Since it went up and came down, we know that it fell for .4 seconds.

s = 1/2 a t^2 = 16 * .016 = .256 feet

v = Vo - at
0 = Vo - 32 * .4 = Vo - 12.8
Vo = 12.8 ft/s

Double check:

s = 12.8t - 16t^2
= t(12.8-16t)
has zeros at t=0, 0.8

Wow - some arm that guy has, eh? Threw the ball 3" up!