Question

An object is thrown from ground level directly upwards with an initial velocity v0.

Prove that the ball will reach its peak exactly halfway through the fall.

Answer 1

Initial velcocity of object is Vo upward. Acceleration is g downward.
When back of the ground, it's displacement = 0
Applying, s = ut +at²/2 taking upward direction as +ve , we get
0 = Vo t_f - gt_f²/2
where t_f is time of flight
t_f = 2Vo/g   ....1

When object is at peak, it's speed = 0. Applying
v = u + at, from starting position to , till it reaches at peak, we get
0 = Vo - gt_p
t_p is time to reach peak
t_p = Vog    .....2
from 1 and 2
t_p = t_f/2