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

Answer 1

The correct option is C $2gH=n{u}^2(n-2)$

Taking upward direction as positive direction.
Time taken to reach the maximum height, $t_1=\frac{u}{g}$
If $t_2$ is the time taken to hit the ground, then
$-H=u{t}_2-\frac{1}{2}g{t}_2^2$
But $t_2=n{t}_1$ (Given)
So, $-H=u\frac{nu}{g}-\frac{1}{2}g\frac{n^2{u}^2}{g^2}$
$-H=\frac{n{u}^2}{g}-\frac{1}{2}\frac{n^2{u}^2}{g}$
$\Rightarrow 2gH=n{u}^2(n-2)$