A river 400 m wide flows at a rate of 2.0 m/s . A boat sails at a velocity of 10 m/s with respect to the water, in a direction perpendicular to the river. Determine the time taken by the boat to reach the opposite bank, in seconds.

Step-by-step solution

The width of the river is d = 400 m . The velocity of the boat with respect to the water is v_ br = 10 m/s . Since the boat sails in a direction perpendicular to the river flow, the component of its velocity along the width of the river is exactly v_ br . The time taken to cross the river is given by the ratio of the width of the river to the component of the boat's velocity perpendicular to the river flow. t = d v_ br t = 400 10 = 40 s