Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 9 - Review Exercises - Page 1036: 59

Answer

a. $x=(100cos40^\circ) t$, $y=6+(100sin40^\circ) t-16t^2$ b. $t=1sec$, $x \approx76.6\ ft$, $y \approx54.3\ ft$; $t=2sec$, $x \approx153.2\ ft$, $y \approx70.6\ ft$; $t=3sec$, $x \approx229.8\ ft$, $y \approx54.8\ ft$. c. $t\approx4.1\ sec$, $x \approx314.1\ ft$ d. $t=2.0\ sec$, $y\approx70.6\ ft$
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Work Step by Step

a. Given $v_0=100, \theta=40^\circ, h=6$ and using the formula in the exercise, we have $x=(100cos40^\circ) t$ and $y=6+(100sin40^\circ) t-16t^2$ b. At $t=1sec$, we have $x=(100cos40^\circ)(1)\approx76.6\ ft$ and $y=6+(100sin40^\circ)(1)-16(1)^2\approx54.3\ ft$. At $t=2sec$, we have $x=(100cos40^\circ)(2)\approx153.2\ ft$ and $y=6+(100sin40^\circ)(2)-16(2)^2\approx70.6\ ft$. At $t=3sec$, we have $x=(100cos40^\circ)(3)\approx229.8\ ft$ and $y=6+(100sin40^\circ)(3)-16(3)^2\approx54.8\ ft$. c. To find the time of flight, let $y=0$. We have $6+(100sin40^\circ) t-16t^2=0$. Solve this equation using a formula or graphically as shown in the top figure. Choosing the positive solution, we have $t\approx4.1\ sec$ and $x=(100cos40^\circ)(4.1)\approx314.1\ ft$ d. Graph the equations as shown in the bottom figure. We can find that the maximum happens at $t=2.0\ sec$, giving $x\approx153.2$ and $y\approx70.6\ ft$ as the maximum height.
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