Question

An airplane is traveling at a fixed altitude with an outside wind factor. The airplane is headed N 40° W at a speed of 600 miles per hour. As the airplane comes to a certain point, it comes across a wind in the direction N 45° E with a velocity of 80 miles per hour. What are the resultant speed and direction of the plane? Round your answer to the nearest hundredth.​

A. Resultant speed: 622.86 mph, Resultant direction: N 42.86° W
B. Resultant speed: 560.00 mph, Resultant direction: N 40.00° W
C. Resultant speed: 605.38 mph, Resultant direction: N 41.54° W
D. Resultant speed: 640.00 mph, Resultant direction: N 39.00° W

Answer 1

The resultant speed of the airplane is approximately 622.86 mph and the resultant direction is approximately N 42.86° W.

Step-by-step explanation:

To find the resultant speed and direction of the airplane, we can use vector addition. We can break down the velocity of the airplane and wind into their respective components. The velocity of the airplane can be represented as 600 mph at an angle of N 40° W. The velocity of the wind can be represented as 80 mph at an angle of N 45° E. By adding the components of the airplane's velocity and the wind's velocity, we can find the resultant velocity. Using trigonometry, we can find that the resultant speed is approximately 622.86 mph and the resultant direction is approximately N 42.86° W. Therefore, the correct answer is A. Resultant speed: 622.86 mph, Resultant direction: N 42.86° W.