A man of height $h$ walks in a straight path towards a lamp post of height $H$ with uniform velocity

Question

A man of height $h$ walks in a straight path towards a lamp post of height $H$ with uniform velocity $u$. Then the velocity of the edge of the shadow on the ground will be\

Professor PC Thomas Classes · Answer

$\mathrm{h}=$ height of man\ $\mathrm{H}=$ height of lamp post\ $	herefore 	an 	heta=\frac{\mathrm{H}-\mathrm{h}}{\mathrm{x}}$\ Also $	an 	heta=\frac{H}{y+x}$\ $	herefore \frac{\mathrm{H}-\mathrm{h}}{\mathrm{x}}=\frac{\mathrm{H}}{\mathrm{y}+\mathrm{x}} \quad \mathrm{Hy}+\mathrm{Hx}-\mathrm{hy}-\mathrm{hx}=\mathrm{HX}$\ $y(H-h)=h x$\ $\frac{\mathrm{dy}}{\mathrm{dt}}=\frac{\mathrm{h}}{\mathrm{H}-\mathrm{h}} \frac{\mathrm{dx}}{\mathrm{dt}}=\frac{\mathrm{hu}}{\mathrm{H}-\mathrm{u}}$\