Question

An airplane is flying in a direction of 75° north of east at a constant flight speed of 300 miles per hour. The wind is blowing due west at a speed of 25 miles per hour. What is the actual direction of the airplane? Round your answer to the nearest tenth. Show your work. PLS PLS PLSPLS HELP URGANT

Answer 1

79.7°

Explanation:

We resolve the speed of the plane into horizontal and vertical components respectively as 300cos75° and 300sin75° respectively. Since the wind blows due west at a speed of 25 miles per hour, its direction is horizontal and is given by 25cos180° = -25 mph. We now add both horizontal components to get the resultant horizontal component of the airplane's speed.

So 300cos75° mph + (-25 mph) = 77.646 - 25 = 52.646 mph.

The vertical component of its speed is 300sin75° since that's the only horizontal motion of the airplane. So the resultant vertical component of the airplane's speed is 300sin75° = 289.778 mph

The direction of the plane, Ф = tan⁻¹(vertical component of speed/horizontal component of speed)

Ф = tan⁻¹(289.778 mph/52.646 mph)

Ф = tan⁻¹(5.5043)

Ф = 79.7°