Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 3 - Exercises and Problems - Page 49: 72


The proof is below.

Work Step by Step

We know the following equation: $x= x_0 + v_{x0}t$ We also know: $ R = \frac{v_0^2sin(2\theta_0)}{g}$ We know that $\Delta x $ and R are the same value, so: $ v_{x0}t=\frac{v_0^2sin(2\theta_0)}{g}$ $ v_{0}cos\theta t=\frac{2v_0^2sin(\theta_0)(cos\theta_0)}{g}$ $ t = 2\frac{v_0sin\theta}{g}$ Here, we see that to land at the same time, $v_0sin\theta$ would have to be the same. Above, we see that to land at the same point, $v_0^2sin(2\theta_0)$ would have to be the same. These will never be equal, so the balls will never land in the same place.
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