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

Answer 1

Answer: (C)

Time taken to reach highest point is $t_{1}=\frac{u}{g}$
Speed on reaching ground $=\sqrt{u^{2}+2gh}$
Now, $v=u+at$
$\Rightarrow \sqrt{u^{2}+2 g h}=-u+gt$
$\Rightarrow t=\frac{u+\sqrt{u^{2}+2 g H}}{g}=\frac{nu}{g}$
$\Rightarrow 2gH=n(n-2) u^{2}$