Question

A man of mass m starts moving w.r.t. a platform of mass 2m with a velocity $u=\frac{9}{13}m/s$ as shown in the figure. The platform is fitted with a concave mirror of focal length f. The velocity of image (in m/s) at the initial moment is :

Answer 1

Magnification $m=\frac{-f}{-f+\frac{3f}{2}}$

$\Rightarrow m=-2$

Taking the direction in the right hand side $V_{im}=-m^2{V}_{om}$

$V_{im}\to velocityofimagew.r.t.mirror$

$V_{om}\to velocityofobjectw.r.tmirror$

$\Rightarrow V_{im}=-4u$

$V_m=\frac{-mu}{m+2m}=-\frac{u}{3}\to velocityofplatform\left(minor\right)$

$V_{im}=V_i-V_m$

$V_i\to velocityofimagew.r.tground$

$\Rightarrow V_i=-4u-\frac{4}{3}$

$V_i=-\frac{13}{3}u$

$V_i=3m/s$