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 how far from the point directly opposite to the starting point the boat reaches the opposite bank, in meters.

Step-by-step solution

Let the width of the river be w = 400 m . The velocity of the boat with respect to the water is v_ br = 10 m/s . Since the boat is steered perpendicular to the river flow, the time taken to cross the river is given by: t = w v_ br = 400 10 = 40 s The river flows at a velocity of v_r = 2.0 m/s . The drift of the boat, which is the distance from the point directly opposite to the starting point, is calculated as: x = v_r t x = 2.0 40 = 80 m