An airplane needs to fly to a destination located exactly 360 km due North of its starting point. A strong wind is blowing due East at a constant speed of 50 km h ⁻¹ . If the speed of the airplane in still air is 130 km h ⁻¹ , the pilot must angle the plane West of North to reach the destination along a straight path. The total time taken for the flight is ______ hours.

Step-by-step solution

Let the airplane's speed in still air be v_a = 130 km h ⁻¹ and the wind speed be v_w = 50 km h ⁻¹ . To travel exactly due North, the Eastward drift caused by the wind must be cancelled by the Westward component of the airplane's velocity. If the plane heads at an angle West of North, then: v_a = v_w 130 = 50 = 5 13 The effective speed of the airplane along the North direction is: v_ eff = v_a = v_a^2 - (v_a )^2 = 130^2 - 50^2 = 120 km h ⁻¹ The time taken to cover the distance of 360 km due North is: t = Distance v_