A tool used to drive fence posts into the ground is known as a ‘post-rammer’. The distances, in millimetres, that the post moves into the ground with each impact of the post-rammer form a geometric progression. The first three impacts make the post sink into the ground by $50\text{ mm}$, $40\text{ mm}$ and $32\text{ mm}$ respectively.
(a)[3]
Verify that the $9$th impact is the first one in which the post sinks less than $10\text{ mm}$ into the ground.
(b)[2]
Find the total depth of the post in the ground after $20$ impacts, giving your answer to the nearest millimetre.
(c)[2]
Find the greatest possible total depth in the ground that could be achieved in theory.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State that $r=0.8$ is the common ratio.” …