Challenging +1.2 This is a standard M4 oblique collision problem requiring resolution of velocities parallel and perpendicular to the wall, application of the restitution formula, and use of the given speed ratio to find the deflection angle. While it involves multiple steps and algebraic manipulation with trigonometry, it follows a well-established method taught in M4 with no novel insight required—making it moderately above average difficulty for A-level but routine for this advanced mechanics module.
A small ball is moving on a smooth horizontal plane when it collides obliquely with a smooth plane vertical wall. The coefficient of restitution between the ball and the wall is \(\frac{1}{3}\). The speed of the ball immediately after the collision is half the speed of the ball immediately before the collision.
Find the angle through which the path of the ball is deflected by the collision. [8]
A small ball is moving on a smooth horizontal plane when it collides obliquely with a smooth plane vertical wall. The coefficient of restitution between the ball and the wall is $\frac{1}{3}$. The speed of the ball immediately after the collision is half the speed of the ball immediately before the collision.
Find the angle through which the path of the ball is deflected by the collision. [8]
\hfill \mbox{\textit{Edexcel M4 2014 Q3 [8]}}