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Two swimmers starts a race. One who reac...

Two swimmers starts a race. One who reaches the point C first on the other bank wins the race. Boy A makes his strokes in a direction of `37^(@)` to the river flow velocity 5 km/hr relative to water. Boy B makes his strokes in a direction of `127^(@)` to the river flow with same relative velocity. River is flowing with speed of 2 km/hr and is 100 m wide. Who will win the race ? Compute the time taken by A and B to reach the point C if the speeds of A and B on the ground are 8 km/hr and 6 km/hr respectively.

Text Solution

Verified by Experts

The correct Answer is:
`B, t_(A)=165s, t_(B)=150 s`
`V_(A)=(4+2)hat(i) +3 hat(j),V_(B)=(-3+2)hat(i) +4 hat(j)`

Time to cross the river `t_(A) =(100)/(3) ,t_(B)=(100)/(4)`
Drift `= (100)/(3) xx 6 = 200 m` , Drift `= -1 xx (100)/(4)`
Remaining distance `= 300 - 200 + 25 m`
`(t_("total"))_(A)=(100)/(3)+(100)/(8) ,t_(B)=(100)/(4)+(100)/(6)`
`t_(A)=(800+300)/(24)=(1100)/(24) ,t_(B)=(600+400)/(24)=(1000)/(24)`
`t_(A) = 165 sec t_(B)=150 sec`.
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