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A,B &C are three objects each moving wit...

`A,B &C` are three objects each moving with constant velocity. A's speed is `10m//sec` in a direction `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`.

Text Solution

Verified by Experts

The correct Answer is:
`5m//s`
`vec(V_(BA))=vec(V_(B))-vec(V_(A)) ...(1)`
`vec(V_(CB)) = vec(V_(C )) - vec(V_(B)) ….(2)`

from (1) & (2) `vecV_(BA) +vecV_(CB) = vecV_(C ) - vecV_(A)`
`rArr vecV_(C) = vecV_(BA) +vecV_(CB) +vecV_(A)`
`|vecV_(C)| = sqrt(V_(BA)^(2)+(|vecV_(CB)+vecV_(A)|)^(2)+2V_(BA)|vecV_(CB)+vecV_(A)|cos(pi-theta))`
`|vec(V_(C))| = sqrt((6)^(2)+(2)^(2)-2xx6xx2xx(1.5)/(24))`
`rArr |vec(V_(C))| = sqrt(36 +4-15)`
`|vec(V_(C))| = sqrt(25) rArr |vec(V_(C)) = 5m//s`
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