A ball is released from a height of $1$ metre, and on hitting the ground it rebounds straight up to $0.96$ metres. It keeps bouncing on the ground, with the maximum height decreasing each time. Two distinct models, $A$ and $B$, are used to describe this.
Model $A$: Each bounce reduces the height reached by $0.04$ metres.
Model $B$: Each bounce reduces the height reached by $4\%$.
(a)[3]
Find the total vertical distance travelled by the ball, counting both upward and downward motion, from the first time it strikes the ground until the $21$st time it strikes the ground, using model $A$.
(b)[3]
Find the total vertical distance travelled by the ball, counting both the ascent and the descent, from the first time it hits the ground until it hits the ground for the $21$st time, using model $B$.
(c)[2]
Show that, under model $B$, even with no limit on the number of bounces, the total vertical distance travelled after the first time it hits the ground cannot be greater than $48$ metres.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Recognise arithmetic series terms” …