Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.2 Exercises: 98


The velocity is $-118$ feet per second after three seconds. The velocity is $-86$ feet per second after falling 108 feet.

Work Step by Step

$s(t)=-16t^2+v_0t+s_0$ $\frac{d}{dt}s(t)=v$ $\frac{d}{dt}s(t)=-32t+v_0$ $v=-32t+v_0$ $v_0=-22$ $v=-32t-22$ After three seconds $(t=3)$, the velocity is: $v=-32(3)-22$ $v=-118$ feet per second When the ball falls 108 feet from a 220-foot building, its 112 feet above the ground. $s_0=220$ $s(t)=112$ $s(t)=-16t^2+v_0t+s_0$ $112=-16t^2+(-22)t+220$ $-16t^2-22t+108=0$ $-8t^2-11t+54=0$ $(2-t)(8t+27)=0$ $t=2$ or $-27/8$ $t$ can't be negative. $t=2$. The ball falls 108 feet after 2 seconds. $v=-32t-22$ $v=-32(2)-22$ $v=-86$ feet per second
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