Two persons (P) and (Q) are standing ` 54 m` apart on a long moving belt. Person (P) rolls a round staone towards person (Q) with a speed of ` 9 ms^(-1)` with respect to belt . If the belt is moving with a speed of `4 ms^(-1)` in the direction from (P) to (Q) (a) What will be the speed of the stone with respect to an obsever on a stationary platform if person (Q) rolls the stone with a velocity of ` 9 ms^(-1)` with respect to the belt towards person (P) and the time taken by the stoine to travel from (Q) to (P) ?

Explanation

(a) Let the direction from (P) to (Q) be positive. Given , speed of the belt, ` v_b =+ 4 ms^(-1)` , speed of the stone w.r.t. belt, ` v_s = + 9 ms^(-1) speed of stpne w.r.t. a stationary observe
` = v_S + v_b = 9 + 4 = 13 ms^(-1)`
(b) Since, persons ` P and Q` are located on belt, the speed of stone w.r.t. `P` or ` Q` will be ` 9 ms^(-1)` . As distance between ` (P) and ` Q= 54 m`, so time taken `= 54//9 = 6 s.
(c ) Here , ` v_b = + 4 ms^(-1)` , v_s =-9 ms^(-1)`
:. Speed of the stone w.r.t. observe
` v_s + v_b =- 9 + 4 =- 5 ms^(-1)`
Here, negative singn shows that the stone is moving in a direction opposite to the direction in which the belt is moving.
In this case also , the speed of stone w.r.t. ` P or ` Q` is still ` 9 ms^(-1)`.
So, time taken ` = ( 534) /9 = 6 s`.