Physics 9702 · AS & A Level · Equations of motion

Equations of motion — practice question

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

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