Question 10
Identical wind turbines are equally spaced in a straight line on level ground. Each turbine tower is a vertical cylinder of radius 1 metre. Let $\mathcal L$ be the line through the base centres of the towers. There is an observer fixed at $O$ on the same level ground as the towers. Let $A$ be the point on $\mathcal L$ that is closest to $O$.
If $A$ is the base centre of a tower and $OA=15$ metres, what is the maximum number of towers that are completely visible to the observer over all possible distances $d$ metres between the base centres of adjacent towers? [5 marks]
Investigation: If $OA=16$ metres and $A$ is not the base centre of a tower, what is the maximum number of towers that are completely visible to the observer? [4 bonus marks]
Written reasoning is required. The reference answer is not an automatic assessment of a student proof.
If $A$ is the base centre of a tower and $OA=15$ metres, what is the maximum number of towers that are completely visible to the observer over all possible distances $d$ metres between the base centres of adjacent towers? [5 marks]
Investigation: If $OA=16$ metres and $A$ is not the base centre of a tower, what is the maximum number of towers that are completely visible to the observer? [4 bonus marks]
Written reasoning is required. The reference answer is not an automatic assessment of a student proof.