Plane A is flying at 600 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) 431 mph
C) 357 mph
D) 100 mph

Question

Quizplus · Accepted Answer

To find the relative speed of Plane B as observed from Plane A, we need to subtract the velocity of Plane A (in the northeast direction) from the velocity of Plane B (in the north direction). 
Let's break the velocity vector of Plane A into its northern and eastern components:
Velocity of Plane A = 600 mph (northeast)
= 600/√2 mph (north) + 600/√2 mph (east) (using trigonometry)

Therefore, the velocity of Plane B as observed from Plane A is:
Velocity of Plane B (relative to A) = Velocity of Plane B - Velocity of Plane A
= 500 mph (north) - (600/√2) mph (north)
= (500 - 600/√2) mph (north)
= 431 mph (north) (approx)

Hence, the answer is (B) 431 mph.

Plane a Is Flying at 600 Mph in the Northeast