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 :

Step-by-step solution

nt AB = t AB + t BC + t CD n - 1 t AB = t BC + t CD         ....(1) n - 1 u g = u g + t CD ∴   n - 2 u g = t CD ...(2) H + h = 1 2 gt BD 2 H + u 2 2 g = 1 2 g n - 1 u g 2 ...from (1) ∴    H + u 2 2 g = n - 1 2 u 2 2 g ∴     H = u 2 2 g n - 1 2 - 1 2g H = nu 2 (n - 2)