Discussion Forum



1)

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

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

Answer:

Option C

Explanation:

 Time taken to reach the maximum height

             t1=u/g

 1532021401_m5.JPG

If t2 is the time taken to hit the ground,

i.e,    $-H=ut_{2}-\frac{1}{2}gt^{2}$

 But               t2=nt1                  [Given]

So, $-H=u\frac{nu}{g}-\frac{1}{2}g\frac{n^{2}u^{2}}{g^{2}}$

       $-H=\frac{nu^{2}}{g}-\frac{1}{2}\frac{n^{2}u^{2}}{g}$

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