(a) For head on collission:

Conservation of momentum ⇒ 2mv_{0} = mv_{1} + mv_{2}

Since e <1 ⇒ v_{1} has the same sign as v_{0}, therefore the ball moves on after collission.

(b) Conservation of momentum ⇒ p = p_{1}+ p_{2}

⇒ p^{2}/2m > p_{2}^{2}/2m + p_{2}^{2}

Thus p, p_{1} and p_{2} are related as shown in the figure.

θ is acute (less than 90°) (p^{2} = p_{1}^{2} + p_{2}^{2} would give θ = 90°)