Plane A is flying at 350 mph in the northeast direction relative to the earth.Plane B is flying at 520 mph in the north direction relative to the earth.What is the direction of motion of Plane B as observed from Plane A?

A) 72.1° N of E
B) 42.2° N or W
C) 47.8° N of W
D) 17.9° N of W
E) 41.1° N of W

Question

Plane A is flying at 350 mph in the northeast direction relative to the earth.Plane B is flying at 520 mph in the north direction relative to the earth.What is the direction of motion of Plane B as observed from Plane A?
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A) 72.1° N of E
B) 42.2° N or W
C) 47.8° N of W
D) 17.9° N of W
E) ​41.1° N of W

Quizplus · Accepted Answer

We need to find the relative motion of Plane B as observed from Plane A. To do this, we need to find the velocity vector of Plane B from the perspective of Plane A.

Let's assume that the velocity of Plane B is made up of two components - one towards the north (as given in the problem) and the other towards the east.

The velocity of Plane B towards east (relative to the earth) is zero because it is not moving eastward. The velocity of Plane A towards east (relative to the earth) is 350 mph towards northeast, which means that the velocity towards the east is 350/sqrt(2) mph.

Therefore, the velocity vector of Plane B as observed from Plane A is the vector sum of its velocity towards north (520 mph) and its velocity towards east (350/sqrt(2) mph).

Using vector addition, we get:

Velocity vector of Plane B as observed from Plane A = sqrt[(520)^2 + (350/sqrt(2))^2] = 605.1 mph

Now, we need to find the angle between this velocity vector and the north-east direction (the direction of Plane A's motion).

Using trigonometry, we get:

tan(theta) = (350/sqrt(2)) / 520 
=> theta = 47.8°

Therefore, the direction of motion of Plane B as observed from Plane A is 47.8° N of W.

Plane a Is Flying at 350 Mph in the Northeast