Question

A body is projected vertically downwards from A,the top of the tower, reaches the ground in t1 seconds.if it is projected upwards with same speed,it reaches the ground in t2 seconds.At what time will it reach the ground if it is dropped from A? ​

Answer 1

Answer:

T = √t1t2

Explanation:

A body is projected vertically downwards from A,the top of the tower, reaches the ground in t1 seconds.if it is projected upwards with same speed,it reaches the ground in t2 seconds.At what time will it reach the ground if it is dropped from A? ​

Let Say Body is Projected with Velocity V downward

& Height of Tower = H

Then H = Vt1 + (1/2)gt1²

if Projected with Velocity V upwards

then time taken to reach top = V/g

Time to come back at same position = 2V/g

=> t2 = t1 + 2V/g

=> V = (t2 - t1)g/2

If it is Dropped then

H = (1/2)gT²

=> Vt1 + (1/2)gt1² = (1/2)gT²

=> t1(t2 - t1)g/2 + (1/2)gt1² = (1/2)gT²

=> t1t2 - t1² + t1² = T²

=> T² = t1t2

=> T = √t1t2

Time taken to reach ground if dropped = √t1t2