Question

A ball of mass m, moving with a speed 2v₀, collides inelastically (e > 0) with an identical ball at rest. Show that 

(a) For head-on collision, both the balls move forward. 

(b) For a general collision, the angle between the two velocities of scattered balls is less than 90°.

Answer 1

(a) For head on collission:

Conservation of momentum ⇒ 2mv₀ = mv₁ + mv₂ 

Since e <1 ⇒ v₁ has the same sign as v₀, therefore the ball moves on after collission.

(b) Conservation of momentum ⇒  p = p₁+ p₂

⇒ p²/2m > p₂²/2m + p₂² 

Thus p, p₁ and p₂ are related as shown in the figure.

θ is acute (less than 90°) (p² = p₁² + p₂² would give θ = 90°)