Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 4 - Two-Dimensional Kinematics - Conceptual Questions - Page 103: 7

Answer

The optimal launch angle is less than $45^\circ$.

Work Step by Step

You can think of an optimal angle for maximum range as a compromise between maximizing flight time (higher angle) and maximizing horizontal component of the velocity (lower angle). This balance is reached at $\theta=45^\circ$ when there is no air resistance. When there is air resistance, then the shorter length of the trajectory (total length of the curve along which the body moves) has to be smaller so that the resistance force does less work, so the optimal angle is then less than $45^\circ$.
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