Question

a ball is thrwon vertically upwards and is caught by the thrower after 5.2seconds. what is the inital velocity

Answer 1

s = ut + 0.5at^2
let downward is positive.
s = 0 ; return to the thrower
t = 5.2
a = g = 10 m/s^2 ; downward

you will get u as negative (upward) otherwise something is wrong.