A motorboat crosses a river, always keeping its heading exactly perpendicular to the river's flow. The speed of the river's flow is 6 m s ⁻¹ and the resultant speed of the boat relative to the ground is 10 m s ⁻¹ . If the boat reaches the opposite bank at a point 120 m downstream from the point directly across its starting position, the width of the river is ______ m .

Step-by-step solution

Let v_r be the velocity of the river and v_m be the velocity of the motorboat in still water. Since the boat heads perpendicular to the flow, its resultant velocity v relative to the ground is given by the vector sum of v_m and v_r which are perpendicular to each other: v = v_m^2 + v_r^2 10 = v_m^2 + 6^2 v_m = 8 m s ⁻¹ The downstream drift x is caused entirely by the river's flow. The time t taken to cross the river is: x = v_r t 120 = 6 t t = 20 s The width of the river w is covered by the boat's velocity componen