A river of width 160 m is flowing with a steady speed of 8 m s ⁻¹ . A motorboat, which has a speed of 10 m s ⁻¹ in still water, is steered at an angle of 127^ with respect to the direction of the river flow. The drift of the boat when it reaches the opposite bank is :

Step-by-step solution

Let the velocity of the river be v_r = 8 m s ⁻¹ and the velocity of the boat in still water be v_b = 10 m s ⁻¹ . The boat is steered at an angle of 127^ with the river flow. We can resolve the boat's velocity into components perpendicular and parallel to the river flow. Perpendicular component of boat's velocity: v_ = v_b (127^ ) = 10 4 5 = 8 m s ⁻¹ Parallel component of boat's velocity: v_ = v_b (127^ ) = 10 (- 3 5 ) = -6 m s ⁻¹ Net velocity of the boat along the river flow (x-direction): v_x = v_r + v_ = 8 - 6 =