`A,B &C` are three objects each moving with constant velocity. A's speed is `10m//sec` in a opposite direction of `vec(PQ)`. The velocity of `B` relative to `A` is `6m//sec` at an angle of, `cos^(-1) (15//24)` to `PQ`. The velocity of `C` relative to `B` is `12m//sec` in a direction `vec(PQ)`, then find the magnitude of the velocity of `C`.

Options

A. `5 m//s`
B. `2sqrt(10) m//s`
C. `3 m//s`
D. `4 m//s`

Answer

A

Explanation

`|vec(v)_(A)|=10 m//s`
`vec(v)_(C)=vec(v)_(C//B)+vec(v)_(B//A)+vec(v)_(A)`
`=12(-hat(i))+6xx15/24(hat(i))+(6xxsqrt(351)/24 hat(j))+10 hat(i)`
`=(15/4-2)hat(i)+sqrt(351)/4 hat(j)`
`|vec(v)_(C)|=sqrt(7^(2)+(sqrt(351))^(2))/(4)=3m//s`