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A ball of mass m, moving with a speed 2 vo , collides inelastically (e > 0) with an identical ball at rest. Show that, (i) for head-on collision, both the balls move forward (ii) for a general collision, the angle between the two velocities of scattered balls is less than 90°.

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(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...
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(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°)

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