On a long horizontally moving belt (Fig. 3.26), a child runs to and for 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 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 answer alter if motion is viewed by one of the parents ?

Explanation

Let us consider left to right to be the positive direction of x-axis.
a) Here, the velocity of belt `upsilon_(B)=+4km//h,`
Speed of child w.r.to belt `upsilon_(C)`
`" "=+9km//h=5/2m//s`
Speed of the child w.r.to stationary observer,
`upsilon_(C)""^(1)=upsilon_(C)+upsilon_(B)=9+4=13km//h`
b) Here, `upsilon_(B)=+4km//h, upsilon_(C)=-9km//h`
Speed of the child w.r.to stationary observer
`upsilon_(C)""^(1)=upsilon_(C)+upsilon_(B)=-9+4=-5km//h`
Here negative sign shows that the child will appears to run in a opposite to the direction of motion of the belt.
c) Distance between the parents S = 540 m
Since parents and child are located on the same belt, the speed of the child as observed by stationary observer in either direction (Either from mother to father (or) from father to mother) will be 9 km/h.
Time taken by child in case (a) and (b) is
`t=50/((5//2))=20S`
If motion is observed by one of the parents, answer to case (a) (Or) case (b) will be altered. It is so because speed of child w.r. to either of mother (or) father is 9 km/h. But answer (c) remains unaltered due to the fact that parents and child are on the same belt and such all are equal affected by the motion of the belt.