# A stone thrown vertically upwards with initial velocity u reaches a height ‘h’ before coming down. Show that the time taken to go up is same as the time taken to come down. - Science and Technology 1

Sum

A stone is thrown vertically upwards with initial velocity u reaches a height ‘h’ before coming down. Show that the time taken to go up is the same as the time taken to come down.

#### Solution

We have v = u + at

and s = ut + 1/2 "at"^2

∴ s = ("v" - "at")"t" + 1/2"at"^2 + 1/2"at"^2

s = ut - 1/2 "at"^2

As the stone moves upward from A → B

S = AB = h, t = t1, a = - g (retardation)

u = u and v = 0

h = 0 - 1/2 (- "g")"t"_1^2

h = 1/2"gt"_1^2

As the stone moves downward from  B → A

t = t2, u = 0, s = h and a = g

h = 1/2"gt"_2^2

"t"_1^2 = "t"_2^2

"t"_1 = "t"_2

Concept: Free Fall
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