Question

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

Answer 1

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Time of Ascent:
The time taken by body thrown up  to reach maximum height h is called as time of ascent.
Let t₁ be time of ascent.
at maximum height , its velocity is zero, V=0
hence , V=u-gt
0=u-gt₁
t1=u/g ------------- (1)
Time of descent:
after reaching the maximum height, the body begins to travel downwards and reaches the ground.
The time taken to by a freely falling body to touch the ground is called time of descent.
Initial velocity for downward journey is zero  , u= 0
let t₂ be time of descent.
s=ut+1/2 gt²
h=0+1/2gt₂²
t2=√2h/g
but, h=u²/2g
so, we get
t₂=√2u²/2g
   =u/g---------------(2)
from equation 1 and 2 we can say
t₁=t₂
the time of ascent is equal to time descent in the case of bodies moving under gravity.

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