Question

Two balls are projected simultaneously with the same speed from the top of a tower-one upwards and the other downwards. If they reach the ground in 6s and 2s, the height of the tower is:

• A. 120 m
• B. 60 m
• C. 80 m
• D. 30 m

Answer 1

The correct option is B 60 m

Lets consider $u$ initial velocity of the ball

Take, $g=10m/s^2$

From 2nd equation of motion at $t=2sec$

$s=ut+\frac{1}{2}g{t}^2$

$s=2u+\frac{1}{2}\times 10\times 2^2$

$s=2u+20$. . . . . . .(1)

Time taken to come back at projection point is $6-2=4sec$

Time to reach the maximum point is $\frac{4}{2}=2sec$

at the maximum height final velocity is zero, $v=0m/s$

$v=u-gt$

$0=u-2\times 10$

$u=20m/s$

From equation 1, we get

$s=2\times 20+20=60m$

The correct option is B.