Plane A is flying at 400 mph in the northeast direction relative to the earth.Plane B is flying at 500 mph in the north direction relative to the earth.What is the speed of Plane B as observed from Plane A?
A)900 mph
B)640 mph
C)357 mph
D)100 mph

Question

Quizplus · Accepted Answer

To find the speed of Plane B as observed from Plane A, we need to calculate the relative velocity. Plane A's velocity can be broken down into components: 400 mph northeast means 400/sqrt(2) mph north and 400/sqrt(2) mph east. Plane B is moving 500 mph north. The relative velocity in the north direction is 500 - 400/sqrt(2) and in the east direction is -400/sqrt(2). The magnitude of the relative velocity is sqrt((500 - 400/sqrt(2))^2 + (-400/sqrt(2))^2) which is approximately 357 mph.

Plane a Is Flying at 400 Mph in the Northeast