Question

If a plane is flying due north at a velocity of 200 miles per hour and encounters a westerly wind of 50 miles per hour, what is the resultant velocity of the plane?

Answer 1

The resultant velocity of a plane flying due north at 200 miles per hour with a 50 miles per hour westerly wind is approximately 206.2 miles per hour, in a northeastward direction, calculated using the Pythagorean theorem.

Step-by-step explanation:

When a plane flies due north at a certain velocity and encounters a wind blowing from a different direction, the resultant velocity of the plane is affected by the wind. In this case, the plane is flying due north at 200 miles per hour and experiences a westerly wind of 50 miles per hour. To find the resultant velocity, we can use vector addition. Since the plane's velocity and the wind's velocity are perpendicular to each other, the resultant velocity can be determined by constructing a right triangle, with the plane's velocity as one leg and the wind's velocity as the other leg. The hypotenuse of this triangle will represent the resultant velocity of the plane.

Using the Pythagorean theorem (a2 + b2 = c2), the resultant velocity (c) can be calculated as follows:
c = √(a2 + b2)
= √(2002 + 502)
= √(40000 + 2500)
= √(42500)
= 206.2 miles per hour (approx.). Therefore, the resultant velocity of the plane is approximately 206.2 miles per hour, northeastward.