Precalculus 2014
54

 PAGE: 498 SET: Exercises PROBLEM: 54

The pilot’s final heading of miles per hour in a direction of due west.

The resultant velocity can be represented by vector The resultant velocity is the sum of the vector representing the initial course plotted by the pilot and the vector representing the wind .

Thus, .

Vector representing the wind .

The wind is blowing from the directed angle of with a velocity miles per hour.

Draw the figure for the situation.

Observe the figure, the wind is blowing at an angle of  with the horizontal.

Component form of a vector is .

Here .

Magnitude of the wind   is .

Substitute above result in .

Find the magnitude of .

Direction and the speed the pilot should set to achieve this resultant is .

Since lies in the third quadrant, then .

Thus, the pilot needs to plot a course of about miles per hour at a directed angle of .

Pilot needs to plot a course of about miles per hour at a directed angle of .

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