Prove that if a body is thrown vertically upwards, then the time of ascent is equal to the time of descent.

Let,

u = Initial velocity

v = Final velocity

h = Height attained

a = acceleration

t = time

Ascent:

Ball thrown upward with velocity u. So, v = 0 at maximum height h. Also a = -g

Now, using v = u + at

0 = u - g

…..1

Where = time of ascent

Also, by using

u = …..2

From equations 1 and 2, we get,

…..A

Descent:

Ball comes down from height h. So, u = 0 and a = g.

So, using v = u + at

v = g …..3

Where = Time of descent

Now, using

v = …..4

From equations 3 and 4, we get,

…..B

From equations A and B, we see that,