A boat crosses a river from one bank A to another bank B which is opposite. The distance between them is D. The speed of water is V_W and that of boat relative to water is V_B . If V_B = 2V_W , the time taken by the boat to cross the river directly along AB is ( 30^ = 1 2 ) , ( 30^ = 3 2 )

Step-by-step solution

Let the boat be steered at an angle upstream with respect to the line AB to cross the river directly. For the boat to move exactly along AB, the component of its velocity parallel to the river flow must cancel the river's velocity V_W . V_B = V_W Given V_B = 2V_W , substituting this yields: 2V_W = V_W = 1 2 = 30^ The net velocity of the boat along the line AB is the component of V_B perpendicular to the river flow: V = V_B = V_B 30^ = V_B ( 3 2 ) The time taken to cross the river of width D is: t = D V = D V_B 3 2