Question

A pilot must fly his plane due north to reach his destination. The plane can fly at 300 km/h in still air. A wind is blowing out of the northeast at 90 km/h.

(a) What is the speed of the plane relative to the ground?

(b) In what direction must the pilot head her plane to fly due north?

Answer 1

The speed of the plane relative to the ground is 300 km/h, and the pilot must head her plane straight north.

Step-by-step explanation:

(a) To determine the speed of the plane relative to the ground, we need to use vector addition. We can break down the velocity of the plane into two components: one in the direction of the wind and one perpendicular to the wind. The component in the direction of the wind would be 300 km/h since it cancels out the wind speed, and the component perpendicular to the wind would be 0 km/h. Therefore, the speed of the plane relative to the ground is 300 km/h.

(b) To find the direction the pilot must head her plane to fly due north, we need to consider the combined effect of the wind and the plane's velocity. Since the wind is blowing out of the northeast, it creates a force that pushes the plane to the southwest. To counteract this force, the pilot must head her plane in the opposite direction, which is straight north.