Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 1 - Introduction, Measurement, Estimating - Problems - Page 18: 32

Answer

50.6 km

Work Step by Step

We can construct a right angle triangle with the three vertices of the earth's center, the balloon, and the point on the horizon. The hypotenuse of the triangle is R+h, where R is the earth's radius and h is the height of the balloon. Let d be the distance from the balloon to the point on the horizon. We can use the Pythagorean theorem to set up an equation and then solve it for d: $R^2 + d^2 = (R+h)^2$ $R^2 + d^2 = R^2 + 2Rh + h^2$ $d^2 = 2Rh + h^2$ $d = \sqrt{2Rh + h^2} = \sqrt{(2)(6400)(0.2)+(0.2)^2} = 50.6~km$
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