Question

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is

• A. $gH=(n-2)u^2$
• B. $2gH=n^2{u}^2$
• C. $gH=(n-2{)}^2{u}^2$
• D. $2gH=n(n-2)u$

Answer 1

The correct option is D $2gH=n(n-2)u$

As height $=H$ in the tower

time taken by particle to reach highest point of its path is$t=u/g$

So, speed on reaching ground

$v^2=2gH$

Now, $v=u+atv=-u+gt=+2gH=-u+gt$

Onsolving $H=u{t}^2+2gH$

In particular

$2gH=n(n-2)u$