Vector Addition Word Problems 2

Question

A Boeing 727 can travel at a speed of 495 miles per hour in still air. If one traveling 30° west of north encounters a wind blowing at 45 miles per hour 15° north of west, find the resulting speed and direction of the plane.

Answer 1

Setup two separate vectors. One for the plane and one for the wind.

Add the x-components and the y-components as follows:'

x = -(747)*sin(30) - (45)cos(15) = -373.5 - 43.66 = -416.97

y = (747)*cos(30) + (45)sin(15) = 646.92 + 11.65 = 658.267

Sketch a new triangle with the above x and y components.

This will show the path of plane, affected by the wind.

The angle is calculated with:

theta = Tan^-1 (658.27/416.9) = 57.65 degrees

OR we can say: 32.35 degrees west of north (90 - 57.65 = 32.35)

The new speed is the magnitude = hypotenuse of the new path

speed = sqrt (416.97² + 658.27² ) = 779.218 mph.