Question

A body is thrown vertically upwards from the top of a tower from point A. It reaches the ground in

time t1. If it is thrown vertically downwards from A with the same speed, it reaches the ground in time

t

2, if it is allowed to fall freely from A, then the time it takes to reach the ground is given by​

Answer 1

Answer:

Let say Ball thrown with Speed V

thrown vertically downwards with V it reaches the ground in time t₂

S = Vt₂ + (1/2)g(t₂)²

thrown vertically upwards from the top of a tower it reaches the ground in time t1

Time taken to come at same point = t₁ - t₂

Time taken to teach top = (t₁ - t₂)/2

Velocity at top = 0

0 = V - g(t₁ - t₂)/2

=> V = g(t₁ - t₂)/2

S = t₂g(t₁ - t₂)/2 + (1/2)g(t₂)²

S = gt₁t₂/2

if fall freely then

S = (1/2)gt²

Equating both

(1/2)gt² = gt₁t₂/2

=> t² = t₁t₂

=> t = √(t₁t₂)