On a long horizontally moving belt (Fig. 3.26), a child runs to and fro with a speed $9 k m h^{- 1}$ (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 $4 k m h^{- 1}$ . For an observer on a stationary platform outside, what is the
a) speed of the child running in the direction of motion of the belt?
b) speed of the child running opposite to the direction of motion of the belt?
c) time taken by the child in (a) and (b) ?
Which of the answers alter if motion is viewed by one of the parents?

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Solution

Speed of the belt, vB = 4 km/h
Speed of the boy, vb = 9 km/h
a) Since the boy is running in the same direction of the motion of the belt, his speed (as observed by the stationary observer) can be obtained as:
vbB = vb + vB = 9 + 4 = 13 km/h
b) Since the boy is running in the direction opposite to the direction of the motion of the belt, his speed (as observed by the stationary observer) can be obtained as:
vbB = vb + (- vB) = 9 – 4 = 5 km/h
c) Distance between the child’s parents = 50 m
As both parents are standing on the moving belt, the speed of the child in either direction as observed by the parents will remain the same i.e., 9 km/h = 2.5 m/s.
Hence, the time taken by the child to move towards one of his parents is 50/2.5 = 20s.
The child and his parents are standing on the same belt and hence, are equally affected by the motion of the belt. Therefore, for both parents (irrespective of the direction of motion) the speed of the child remains the same i.e., 9 km/h.
For this reason, it can be concluded that the time taken by the child to reach any one of his parents remains unaltered.

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