Buses A and B are moving in the same direction with speed `20 ms^(-1)` and `15 ms^(-1)` respectively. Find the relative velcoity of A w.r.t. B and relative velocity of B w.r.t. A.

Options

A. `(15 ms^(-1))hat(i)` `(-5 ms^(-1))hat(i)`
B. `(5 ms^(-1))hat(i)` `(-15 ms^(-1))hat(i)`
C. `(5 ms^(-1))hat(i)` `(-5 ms^(-1))hat(i)`
D. `(5 ms^(-1))hat(i)` `(15 ms^(-1))hat(i)`

Answer

C

Explanation

Let their direction of motion of bus A is `hat(i)`, then
`v_(A)=(20 ms^(-1))hat(i)` and `v_(B)=(15 ms^(-1))hat(i)`
(i) Relative velocity of A w.r.t. B
`v_(AB)=v_(A)-v_(B) = ("actual velocity of A") - ("velocity of B")`
`=(20 ms^(-1))hat(i)-(15 ms^(-1))hat(i)=(5 ms^(-1))hat(i)`
(ii) Relative velocity of B w.r.t. A
`v_(BA)=v_(B)-v_(A)= ("Actual velocity of B") - ("velocity of A")`
`=(15 ms^(-1))hat(i)-(20 ms^(-1))hat(i)=(-5 ms^(-1))hat(i)=(5 ms^(-1))(-hat(i))`