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A boat crosses a river from port A to po...

A boat crosses a river from port A to port B, which are just on the opposite side. The speed of the water is `V_W` and that of boat is `V_B` relative to still water. Assume `V_B = 2V_W`. What is the time taken by the boat, if it has to cross the river directly on the AB line

A

`(2D)/(V_B sqrt3)`

B

`(sqrt3 D)/(2V_B)`

C

`(D)/(V_B sqrt2)`

D

`(Dsqrt2)/(V_B)`

Text Solution

Verified by Experts

The correct Answer is:
A

For shortest distance
`v_B sin theta = v_w`
`rArr sin theta = (v_m)/(v_b) = 1/2 rArr theta = 30^@`
time taken to cross the river
`t = (D)/(V_B cos theta ) = (D)/(V_B sqrt3 // 2) = (2D)/(sqrt3 V_B)`
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