   Chapter 1, Problem 56P

Chapter
Section
Textbook Problem

An airplane flies 2.00 × 102 km due west from city A to city B and then 3.00 × 102 km in the direction of 30.0° north of west from city B to city C. (a) In straight-line distance, how far is city C from city A? (b) Relative to city A. in what direction is city C? (c) Why is the answer only approximately correct?

(a)

To determine
The distance from city C to city A.

Explanation

Given Info: The airplane flies 2×102km due west from city A to city B. And then 3×102km in the direction of 30° north of west from city B to city C. The x and y position of the airplane is 460km and 150km respectively.

Explanation:

The x position of the airplane is,

x=(200km)+[(300km)(cos(30))]=460km

The y position of the airplane is,

y=(0km)+[(300km)(sin(30))]=150km

Thus, x and y position of the airplane is 460km and 150km respectively

(b)

To determine
The direction of city C relative to city A.

(c)

To determine
The correctness of the distance between city C and city A.

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