On a long horizontally moving belt (Fig. 3.26), a child runs to and fro with a speed 9 km/h (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. 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?
Given,
Relative speed of child with respect to belt, vbc = 9 km/h
Speed of the belt, v = 4 km/h
Distance between parents, d = 50 m
(a) Speed of the child for stationary observer when he moves in same direction of belt is given by, V = vbc + v
= 9 + 4 = 13 km/h
(b) Speed of the child for stationary observer when he moves in opposite direction of belt is given by, V = vbc – v
= 9 – 4 = 5 km/h
(c) Since, parents are stationary with respect to belt, child speed is same for both. That is vbc = 9 km/h = 2.5 m/s
⇒ time taken by child to move towards one of his parents, t = 
∴ t = 
= 20 s
If the motion is viewed in parent’s perspective, answer in (a) and (b) will alter and answer in (C) unaltered. Because, for them child speed is constant and equal to 9 km/h.