Question

A man walking with a speed of 3 m/s passes under a lamp hanging at a height of 8 m above the ground. If the height of the man is 2 m, the velocity in m/s with which the edge of the shadow of the man's head moves over the ground is

Answer 1

Let H be the height of the lamp and h be the height of the man


Then, from the figure,

$\frac{H}{x_s}=\frac{h}{x_s-x}=\tan \theta \Rightarrow H(x_s-x)=h{x}_s\Rightarrow x_s(H-h)=Hx\Rightarrow x_s=\frac{H}{H-h}xTakingderivativeonbothsides{u}_s=\frac{H}{H-h}u=\frac{8}{8-2}\times 3m/s\Rightarrow u_s=4m/s$