Plane A is flying at 350 mph in the northeast direction relative to the Earth.Plane B is flying at 460 mph in the north direction relative to the Earth.What is the direction of motion of Plane B as observed from Plane A?
A)70.7° N of E
B)49.3° N of W
C)40.7° N of W
D)19.3° N of W
E)48.2° N of E

Question

Quizplus · Accepted Answer

To find the direction of motion of Plane B as observed from Plane A, we need to find the vector sum of the velocities of both planes.

Let's break down the velocities into their northward and eastward components.

Plane A: 
Velocity = 350 mph 
Northerly component = 350 cos(45) = 247.5 mph 
Easterly component = 350 sin(45) = 247.5 mph

Plane B: 
Velocity = 460 mph 
Northerly component = 460 
Easterly component = 0

Now we add the velocities:

Northerly component: 460 + 247.5 = 707.5 mph 
Easterly component: 0 + 247.5 = 247.5 mph

Using these components, we can find the direction of the resultant vector:

tan(theta) = (Northerly component)/(Easterly component) = 707.5/247.5 = 2.857

theta = tan^-1(2.857) = 70.7° N of W

Therefore, the answer is C) 40.7° N of W.

Plane a Is Flying at 350 Mph in the Northeast