An aeroplane is required to travel from a point A to another point B , located 500 km away due 30^ east of north. A wind blows due north at a speed of 20 m/s , and the air-speed of the plane is 150 m/s . Determine the direction in which the pilot should head the plane to reach point B .

Step-by-step solution

Let v _ p be the velocity of the plane with respect to the ground, v _ w be the velocity of the wind, and v _ pw be the velocity of the plane with respect to the wind. We are given that v _ p = v _ pw + v _ w . Let the north direction be along the y-axis ( j ) and the east direction be along the x-axis ( i ). The wind velocity is v _ w = 20 j . Let the plane head at an angle east of north. The velocity of the plane with respect to the wind is: v _ pw = 150 i + 150 j The velocity of the plane with respect to the gro