A plane is moving due north,directly towards its destination.Its airspeed is 200 mph.A constant breeze is blowing from west to east at 42 mph.In which direction is the plane pointed?
A) 5.7° W of N
B) 12° W of N
C) 22° W of N
D) 11° E of N

Question

Quizplus · Accepted Answer

To solve this problem, we need to use vector addition. Let's break down the velocities into components:

- Airspeed (200 mph) directly North: 0 mph West, 200 mph North
- Breeze (42 mph) West to East: 42 mph East, 0 mph North

We can add these two vectors to get the resulting velocity:

- Resulting velocity: 42 mph East, 200 mph North

To find the direction of this velocity, we can use trigonometry. The angle between this velocity and due North is:
theta = arctan(42/200) = 12.1°

Therefore, the plane is pointed 12° West of North, which corresponds to choice B.

A Plane Is Moving Due North,directly Towards Its Destination