On a long horizontally moving belt, a child runs to and fro with … - Vidyadip

MCQ

On a long horizontally moving belt, a child runs to and fro with a speed $9\, km\, h^{-1}$ (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 $4\, km\, h^{-1}$. For an observer on a stationary platform, the speed of the child running in the direction of motion of the belt is ..... $km\,h^{-1}$

A
$4$
B
$5$
C
$9$
✓
$13$

✓

Answer

Correct option: D.

$13$

d
Figure shows conditions of the quation.

In this case,

speed of belt w.r.t. ground $\therefore v_{B C}=4 \mathrm{\,km} \mathrm{h}^{-1}$

Speed of child wr.t. belt $\quad \therefore v_{C B}=9 \mathrm{\,km} \mathrm{h}^{-1}$

$\therefore$ For an observer on a stationary platform, speed of child running in the direction of motion of the belt is $\mathrm{v}_{\mathrm{CG}}=\mathrm{v}_{\mathrm{CB}}+\mathrm{v}_{\mathrm{BG}}=9 \mathrm{\,km} \mathrm{h}^{-1}+4 \mathrm{\,km} \mathrm{h}^{-1}=13 \mathrm{\,km} \mathrm{h}^{-1}$

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