Question

A cyclist observes a passenger in a bus. He finds that the passenger closed his glass window displacing $20 \,cm$ in forward direction with constant speed, in $1 \,s$. Bus overtakes the cyclist in $3\,s$. Initially he was at the middle of the bus as shown in the figure. Length of the bus is $18\, m$. Both cyclist and bus are moving with constant speed in the same direction. The velocity (in $m / s$ ) of the glass window with respect to cyclist was

Answer 1

Let's designate $V_{m}, V_{B}$ and $V_{W}$ as the speeds of man, bus and window, respectively, with respect to ground.
Clearly, $9 m =\left(V_{B}-V_{m}\right) \times 3\,\,\,...(i)$
and for bus and window:
$\frac{20}{100}=\left[V_{W}-V_{B}\right] \times 1\,\,\,...(ii)$
Adding (i) and (ii), we get
$V_{W}-V_{m}=3.2=V_{W m}$