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

Quizplus · Accepted Answer

To find the speed of Plane B as observed from Plane A, we need to find the resultant velocity of Plane B relative to Plane A.

We can use vector addition to add the velocities of Plane A and Plane B.

Let's take a coordinate system with the x-axis pointing east and y-axis pointing north.

Velocity of Plane A = 440 mph at 45 degrees north of east 
= 440(cos 45 i + sin 45 j) mph

Velocity of Plane B = 550 mph at 90 degrees north 
= 550(j) mph

Adding the two velocities, we get:

Relative velocity of Plane B w.r.t. Plane A 
= (440cos45 + 550) j mph 
= 392 j mph

So, the speed of Plane B as observed from Plane A is 392 mph.

Therefore, the answer is (C).

Plane a Is Flying at 440 Mph in the Northeast