Question

A particle is dropped from the top of a tower of height h and at the same moment of time a second particle is projected upwards from the bottom of the tower. The two particles meet when the first one has descended a distance of h/n. The velocities of these particles, when they meet, are in the ratio

(1) v₁ : v₂ = 2 : (n - 2)

(2) v₁ : v₂ = (n - 2) : n

(3) v₁ : v₂ = √2 : (n - 2)

(4) v₁ : v₂ = 1 : (n-1)

Answer 1

(1) v₁ : v₂ = 2 : (n - 2)

When the two particles meet we have for the first particle,

and for the second particle

Adding Eqn, (1) and (2), we have

Substituting value of t given by Eqn. (3) in Eqn. (1), we get

At time t, when the two particle meet for the first particle

For the second particle, we have,

From Eqn s. (5) and (6), we have