Answer to Question #311197 in Classical Mechanics for Anonymity

Question

Question #173223 in Physics

Given

Mass(a) = Mass(b)

V(a)1 = 6.2 m/s

V(a)2 = final velocity of the cue ball

V(b)1 = 0 m/s

V(b)2 = final velocity of the billiard ball

angle deflected of the billiard ball = 45° from the horizontal

x = angle deflected of the cue ball from the horizontal

6.2 m/s = (Va2){cos(x) + sin(x)}

In the x-direction

6.2 m/s + 0 m/s = (Va2)(cos x) + (Vb2)(cos 45)

The direction of the cue and billiard balls are the same because of the law of inertia.

In the y-direction

0 m/s + 0 m/s = (Va2)(sin x) + (-Vb2)(cos 45)

The final velocity of the billiard ball in the y-direction is negative because of the difference in the y-direction between the cue and billiard balls.

If we use substitution and elimination methods for two equations we can find 6.2 m/s = (Va2){cos(x) + sin(x)}.

However, I am having difficulty in the next sequence. In which part am I wrong? What is the solution? Do we have to use the formula of coefficient of restitution? I need your help. Thank you.

Answer 1

$6.2=v_{a2}(\cos x +\sin x),$

$6. 2+0=v_{a2}\cos x+v_{b2}\cos 45°,$

$0+0=v_{a2}\sin x-v_{b2}\cos 45°,$

$\cos x=\sin 45°,$ $\implies x=45°,$

$v_{a2}=6 .2(\cos x+\sin x)=8.8~\frac ms.$