Question

A man of height 2 meters walks at a uniform speed of 6 km/hr away from a lamp post of 6 meters high. Find the rate at which the length of the shadow is increasing.

Answer 1

Let OA be the lamp post, MN the man, MB = x, his shadow, and OM = y, the distance of the man from the lamp post at time t.

Then dy/dt = 6 km/hr is the rate at which the man is moving at away from the lamp post.

dx/dt is the rate at which his shadow is increasing.

From the figure,

Hence, the length of the shadow is increasing at the rate of 3 km/hr.