A ball of mass \(m\) moving with a velocity \(v_{1}\) strikes normally a massive rock of mass \(M( > > m)\)…
A ball of mass \(m\) moving with a velocity \(v_{1}\) strikes normally a massive rock of mass \(M( > > m)\) moving towards the ball with a velocity \(v_{2}\). If the collision is perfectly elastic, the magnitude of the velocity of the ball after impact is
\(v_{1}+v_{2}\)
\(v_{1}-v_{2}\)
\(v_{1}+2 v_{2}\)
\(v_{1}-2 v_{2}\)
Solution
For a perfectly elastic one-dimensional collision, the velocity of the ball after the colision is
\(v_{1}=\left(\frac{m-M}{m+M}\right) u_{1}+\frac{2 M\left(-u_{2}\right)}{m+M}\)
Since \(M > > m\),
\(v_{1}=-u_{1}-2 u_{2}=-\left(u_{1}+2 u_{2}\right)\)
The magnitude of \(v_{1}\) is
\(v_{1} \mid=u_{1}+2 u_{2}\)