Question

A man 2 m tall is walking away from a lamppost which is 6m tall at a rate of 2 m/s. Find the rate of change of a)the tip of the shadow b) the length of his shadow

Answer 1

Call distance of man from lamp post x and distance of shadow tip from lamp post y.
Then by similar triangles:
(y-x)/2 = y/6
6 y - 6 x = 2 y
y = 1.5 x
we know dx/dt = 2
dy/dt = 1.5 * dx/dt = 3
dy/dt - dx/dt = speed of tip = 3-2 = 1