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Q.

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

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a

$gH = (n - 2)^{2} u^{2}$

b

$2 gH = {nu}^{2} (n - 2)$

c

$2 gH = n^{2} u^{2}$

answer is C.

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Detailed Solution

detailed_solution_thumbnail

$t_{1} = \frac{u}{g}$

If t₂ is the time taken to hit the ground,

i.e., $- H = {ut}_{2} - \frac{1}{2} {gt}_{2}^{2}$

But $t_{2} = {nt}_{1}$

$\begin{array}{l} - H = \frac{{nu}^{2}}{g} - \frac{1}{2} \frac{n^{2} u^{2}}{g} \\ \Rightarrow 2 gH = {nu}^{2} (n - 2) \end{array}$

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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