Question

Small plane flies at 200 km/h in still air. If the wind blows directly out of the west at 50 km/h,

(a) in what direction must the pilot head her plane to move directly north across land and
(b) how long does it take her to reach a point 300 km directly north of her starting point?

Answer 1

To move north across land, the pilot must head her plane slightly to the right of north. The angle between the plane's heading and due north is calculated using arctan(wind speed / plane speed). The time taken to travel 300 km directly north is 1.46 hours.

Step-by-step explanation:

To move directly north across land, the pilot must head her plane in a direction that offsets the wind. Since the wind is blowing from the west, the pilot should head her plane slightly to the right of north.

The angle between the plane's heading and due north is given by the arctan(wind speed / plane speed). In this case, arctan(50 km/h / 200 km/h) = 14.04°. So the pilot must head her plane at an angle of about 14.04° relative to due north.

To calculate the time taken, we can determine the effective ground speed of the plane. The ground speed is given by the hypotenuse of the right triangle formed by the plane's speed and the wind's speed. Using the Pythagorean theorem, we have sqrt(200^2 + 50^2) = 205.03 km/h. Therefore, the time taken to travel 300 km is 300 km / 205.03 km/h = 1.46 hours.