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,