Ona 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 50m apart on the moving belt. The belt moves with a speed on the moving belt. The belt moves with a speed of 4 km `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 after if motion is viewed by one of the parents?

Explanation

Speed of child w.r.t. belt =9 km `h^(-1)`
Consider the direction from left to right is taken to be positive direction
(a) `v_(C)=+9km h^(-1), v_(B)=+4km h^(-1)`
`therefore` Speed of child w.r.t. stationary observer
`=9+4=13km h^(-1)`
`therefore` Speed of child w.r.t. stationary observer
`=-9+4=-5km h^(-1)`
(c ) Distance between parents =50m
As parents and child are located on the same belt, therefore, speed of child with respect to either parent will be same in either direction and will be `9 km h^(-1)`
`t=(50xx3600)/(9xx1000)`
=20s.
If the motion is viewed by any one of the parents, answer to (c ) is unaltered because the parents and the child are located at the same belt while the answers to a and b will change because the relative velocity of the child is `9 km h^(-1)` as observed by one of parents.