From a tower of height H, a particle is thrown vertically upward 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:

When a particle is thrown vertically upwards with a speed u , at height point the velocity of the particle will be zero.Using   v = u + at0 = u−gt  ⇒ t = ug−−−(i)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 Let t1 = ntUsing, s = ut1+12at12⇒ −H = u(nt)−12g(nt)2⇒ −H = u×n(ug)−12gn2(ug)2     [using(i)]⇒ 2gH = 2nu2−n2u2  ⇒2gH = nu2(n−2)