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 time taken by the plane to go from A to B in minutes.

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 know that v _p = v _ pw + v _w , which can be rearranged as v _ pw = v _p - v _w . The direction of v _p is 30^ east of north, and the direction of v _w is due north. The angle between v _p and v _w is 30^ . Using the cosine rule for the vector triangle: v_ pw ^2 = v_p^2 + v_w^2 - 2 v_p v_w (30^ ) Substituting the given values ( v_ pw = 150 m/s , v_