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 - Problems and Conceptual Exercises - Page 104: 13

Answer

The gravitational acceleration is $$g_Z=1.77\text{ m/s}^2.$$

Work Step by Step

The horizontal distance is covered with the constant velocity (we suppose that the gravitational acceleration is strictly vertical) so we have $$d_h=v_ht\Rightarrow t=\frac{d_h}{v_h}.$$ Now, the vertical distance is covered with uniform gravitational gravitational acceleration $g_Z$ so we have $$d_v=\frac{1}{2}g_Z t^2=\frac{1}{2}g_Z\frac{d_h^2}{v_h^2}=\frac{g_Zd_h^2}{2v_h^2}$$ which yields $$g_Z=\frac{2d_vv_h^2}{d_h^2}=\frac{2\cdot1.40\text{ m}\cdot 6.95^2(\text{ m/s})^2}{8.75^2 \text{ m}^2}=1.77\text{ m/s}^2.$$
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