Question

An airplane heading due east has a velocity of 210 miles per hour. A wind is blowing from the north at 38 miles per hour. What is the resultant velocity of the airplane? (Assume that east lies in the direction of the positive x-axis and north in the direction of the positive y-axis.)

Answer 1

The resultant velocity of the airplane is 213.410 miles/hour and is 10.36° from east.

Explanation:

Given : An airplane heading due east has a velocity of 210 miles per hour.

A wind is blowing from the north at 38 miles per hour.

To Find: What is the resultant velocity of the airplane?

Solution:

Velocity of airplane = 210 miles per hour

Velocity of wind blowing from north = 38 miles per hour

Resultant velocity =
`√((210)^2+(38)^2)`

=
`213.410`

To find the angle of direction

We are given that east lies in the direction of the positive x-axis and north in the direction of the positive y-axis.

So,
`tan \theta = (y)/(x)=(38)/(210)=0.1809 rad`

1 radian = 57.2958 degree

So, 0.1809 rad= 0.1809 * 57.2958=10.36°

Hence the resultant velocity of the airplane is 213.410 miles/hour and is 10.36° from east.