Plane A is flying at 440 mph in the northeast direction relative to the earth.Plane B is flying at 550 mph in the north direction relative to the earth.What is the speed of Plane B as observed from Plane A?

A) 570 mph
B) 916 mph
C) 392 mph
D) 704 mph
E) 714 mph

Question

Plane A is flying at 440 mph in the northeast direction relative to the earth.Plane B is flying at 550 mph in the north direction relative to the earth.What is the speed of Plane B as observed from Plane A?
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A) 570 mph
B) 916 mph
C) 392 mph
D) 704 mph
E) ​714 mph

Quizplus · Accepted Answer

First, we must find the vectors of each plane's velocity. Let us use the origin as the starting point of the two planes, for simplicity.

Plane A is traveling at 440 mph in the northeast direction. This can be represented by a vector with a magnitude of 440 mph and an angle of 45 degrees (northeast is halfway between north and east).

Plane B is traveling at 550 mph in the north direction. This can be represented by a vector with a magnitude of 550 mph and an angle of 90 degrees.

To find the relative velocity of Plane B as observed from Plane A, we simply need to subtract the vectors pointing from the origin to each plane.

Using trigonometry, we can find that the components of Plane A's velocity vector are 311.1 mph to the east and 311.1 mph to the north (this can be found by multiplying the magnitude of 440 by cos(45) and sin(45), respectively).

Similarly, the components of Plane B's velocity vector are 0 mph to the east and 550 mph to the north.

Subtracting the two vectors, we get a result of 311.1 mph to the east and 238.9 mph to the north.

Using the Pythagorean theorem, we find that the magnitude of this vector is approximately 392 mph.

Therefore, the speed of Plane B as observed from Plane A is approximately 392 mph, which corresponds to choice C.

Plane a Is Flying at 440 Mph in the Northeast