Question

A stone dropped from the top of a tower is found to travel 716 of the height of the tower during the last second of its fall. The time of fall is:

Answer 1

Answer: 4s

Explanation:

Let the height be H.

The body fell 7/16 of H

So the height to which body fell is

H-7/16H

=9/16H

Let the time taken to reach the ground is t seconds.

Time at last second = t-1

From second equation of motion

H = ut+1/2at²

When body is dropped u is zero...

H= 1/2at²------(1)

Distance covered in last second

9H/16= 1/2a(t-1)²-----(2)

Dividing (1) by (2) we get..

16/9=t²/(t-1)²

By solving,

7t²-32t+16=0

By solving the quadratic equation we get...

t = 4s