Chapter 12.2, Problem 34E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

The magnitude of a velocity vector is called *speed*. Suppose that a wind is blowing *from* the direction N45°W at a speed of 50 km/h. (This means that the direction from which the wind blows is 45° west of the northerly direction.) A pilot is steering a plane in the direction N60°E at an airspeed (speed in still air) of 250 km/h. The *true course*, or *track*, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The *ground speed* of the plane is the magnitude of the resultant. Find the true course and the ground speed of the plane.

To determine

**To find**: The true course and ground speed of plane.

Explanation

**Given data:**

The speed of wind is

**Formula used:**

Consider the two two-dimensional vectors such as

The vector sum of two vectors

Here,

*x*-coordinates, and

*y*-coordinates.

Write the expression for magnitude of vector

Write the expression for angle of vector **a**

Consider the east direction is located on positive *x*-axis and north direction is located on positive *y*-axis.

Draw the vector diagram of velocities as shown in Figure 1.

From Figure 1, write the expression for velocity vector of wind

Here,

Substitute

From Figure 1, write the expression for velocity vector of plane

Here,

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P-38RECh-12 P-1PCh-12 P-2PCh-12 P-5P

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