Let OA be the lamp post, MN the man, MB = x his shadow and OM = y the distance of the man from lamp post at time t.
Then dy/dt = 3/4 is the rate at which the man is moving towards the lamp post.
dx/dt is the rate at which his shadow is shortening.
B is the tip of the shadow and it is at a distance of x + y from the post.
is the rate at which the tip of the shadow is moving.
From the figure,
45x = 15x + 15y
30x = 15y
Hence (i) the shadow is shortening at the rate of (3/8) metre/sec, and
(ii) the tip of shadow is moving at the rate of (9/8) metres/sec.
