Question

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

Answer 1

Answer:

Suppose the body is thrown up by velocity "u".

Let h be the height it travelled. Reaching height h,it will be at 0 velocity.

According to energy conservation :

mgh = mu²/2

⇒ u² = 2 gh

⇒ h = u²/2g .........(1)

By Laws of Motion :

⇒ v1 = u - gt

⇒ u = gt [ v1=0]

⇒ t = u/g

Now let the velocity reached when the body falls be v.

v² = u2² + 2 gh

⇒ v² = 2 gh [ u2 = 0 for this ]

⇒ h = v²/2g .........(2)

So we have v = u from (1) and (2) :

v = gt

⇒ t = v/g

⇒ t = u/g

And hence time is same in both cases.

Proved.