On a long horizontally moving belt (From figure) a child runs to and fro with a speed 9 `kmh^(-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 kmh-l. 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 ?

Explanation

Suppose, right side is positive direction.
Speed of child w.r.t. belt `v_(c) = 9 kmh^(-1)` and speed of belt `v_(b) = 4 kmh^(-1)`
(a) When boy moves in direction of motion of belt, relative speed od child w.r.t. stationary observer.
`v._(c)=v_(c)+v_(b)`
`= 9 + 4 = 13 kmh^(-1)`
(b) When boy moves opposite to motion of belt, relative speed of child w.r.t. stationary observer.
`v.._(c)=v_(c)+v_(b) =- 9+4 =-5 kmh^(-1)`
Here, negative sign shows that child is moving in opposite to belt.
(c ) Distance between his mother and father,
`s = 50 m=0.05 km`
As child and mother-father are on same belt then speed of child w.r.t. mother-father is `9 kmh^(-1)`
`therefore v =9 kmh^(-1)`
Time taken by child in case (a) and (b)
`t = s/v -= (0.05)/(9)` hour
`therefore t = (0.05 xx 3600)/(9)` second
`therefore t = -20 s`
The answer will not be different in (a) and (b) because in both cases the respective speed of child is `9 kmh^(-1)` w.r.t. mother father.