A ball is projected vertically upwards towards a ceiling and then bounces back, as shown in Fig. 3.1. It is launched with speed $9.6\,\text{m s}^{-1}$ and needs $0.37\,\text{s}$ to get to the ceiling. It remains in contact with the ceiling for a further $0.085\,\text{s}$ before departing with speed $3.8\,\text{m s}^{-1}$. The ball has mass $0.056\,\text{kg}$. Air resistance may be ignored.
(a)[1]
Show that the ball reaches the ceiling with a speed of $6.0\,\text{m s}^{-1}$.
(b)[2]
Calculate the height of the ceiling above the point where the ball was thrown.
(c(i))[2]
Calculate the increase in gravitational potential energy of the ball as it moves from its starting position to the ceiling.
(c(ii))[2]
Calculate the decrease in kinetic energy of the ball while it is in contact with the ceiling.
(d)[2]
State how Newton’s third law applies to the collision between the ball and the ceiling.
(e)[2]
Calculate the change in momentum of the ball during the collision.
(f)[2]
Determine the magnitude of the average force exerted by the ceiling on the ball during the collision.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies $v = u + at$” …