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 = nu²(n-2) 

(b) gH = (n-2)u² 

(c) 2gH = n²u² 

(d) gH = (n-2)²u²

Answer 1

(a) 2gH = nu²(n-2) 

We know that the particle will take a time t₁ = (=u/g) to reach the highest point (for which v = 0). Let t₂ be the time taken by the particle to hit the ground. Then

-H = ut₂ + 1/2 (-g)\(t^2_2\)

We are given that t₂ = nt₁ . 

This gives 2gH = nu²(n-2)