Question

prove that time of ascent is equal time of descent

Answer 1

let the velocity at the time of throwing be U
thus the time for the velocity to become 0 at the highest point of flight.
Thus by first equation of motion thus t1 = U/g
Height attained, H = U2/2g uisng the second equation of motion
Now at the time the time of descent,
time taken for the ball to come down will be:
t22 = 2H/g using the third equation of motion
thus t2 = (U/g)2

clearly t1 = t2