On a long horizontally moving belt, a child runs to and fro with a speed $9 \mathrm{~km} \mathrm{~h}

Question

On a long horizontally moving belt, a child runs to and fro with a speed $9 \mathrm{~km} \mathrm{~h}^{-1}$ (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of $4 \mathrm{~km} \mathrm{~h}^{-1}$. For an observer on a stationary platform, the speed (in $\mathrm{km} \mathrm{h}^{-1}$ ) of the child running in the direction of motion of the belt is

Professor PC Thomas Classes · Answer

(d) : Figure shows conditions of the question. In this case, Speed of belt w.r.t. ground, $v_{B G}=4 \mathrm{~km} \mathrm{~h}^{-1}$ Speed of child w.r.t. belt, $v_{C B}=9 \mathrm{~km} \mathrm{~h}^{-1}$ ∴ For an observer on a stationary platform, speed of child running in the direction of motion of the belt is \ $ v_{C G}=v_{C B}+v_{B G}=9 \mathrm{~km} \mathrm{~h}^{-1}+4 \mathrm{~km} \mathrm{~h}^{-1}=13 \mathrm{~km} \mathrm{~h}^{-1} $