2026 CVSS P1 Q9

A vertical lamp post of height, 6 meters, cast a shadow of length, \(s\) meters, of a man of height 1.8 meters walking away from the lamp post at a uniform speed of 1.5 meters per second. \(x\) meters is the distance of the man from the lamp post.

1. Show that \(s=\dfrac37x\).[2]
2. Find the rate at which the length of his shadow is increasing.[2]
3. Given that \(\theta\) is the angle of elevation from tip of shadow, \(T\) to the top of the lamp post.
   1. Express \(\tan\theta\) in terms of \(x\).[2]
   2. Find the rate of change of angle \(\theta\), in radians per second, at the instant when the man is 3 meters away from the lamp post.[5]