Sol.

In the diagrams, tan α = ⇒

and tan β = ⇒

Taking inclined axes as shown,

=

x = y = Vt –

When the particle hits the plane at A, y = 0,

i.e., Vt – g = 0 ⇒ t =

Therefore, at A, = V – g (3V /5g) = V

= V – g (3V /g) = – V

We can now investigate the effect of the impact

Using the law of restitution perpendicular to the plane gives

v = e

Parallel to the plane the velocity component is unchanged.

Just after impact, the resultant velocity of P is inclined to the plane at an angle θ , where

tan θ = v ÷ = ÷ = 3e

If P continues to move up the plane then

θ < φ ⇒ tan θ < tan φ

Now φ = π – α ⇒ tan θ = cot α

Therefore tan θ < cot α

i.e., 3e < 2

⇒ e <

We also know that e ≥ 0, therefore the range of value s of e for which P continues to move up the plane after impact is

0 < e < .