Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 13 - Vector Functions - 13.4 Motion in Space: Velocity and Acceleration - 13.4 Exercises - Page 919: 31


$(250, -50,0)$ ; $10\sqrt{93} m/s \approx 96.4 ft/s$

Work Step by Step

$v=u+(\lt0,-4,-32 \gt \lt 50,0,80 \gt)t$ [ velocity-time equation, that is $v=u+at$] Thus, $v=\lt 50,-4t,80-32t \gt$ Also, $r(t)=\int v(t)=\lt 50t,-2t^2,80t-16t^2 \gt$ Equate the equations such as: $80t=16t^2=0$ This yields, $t=5$ Now, $r(5)=\lt 50(5),-2(5)^2,80(5)-16(5)^2 \gt$ or, $r(5)=\lt 250, -50,0 \gt$ This yields:$v(5)=\lt 50, -20,-80 \gt$ Need to find the final speed. $|v(5)|=\sqrt {(50)^2+( -20)^2+(-80)^2 }$ or, $=\sqrt {100+400+6400}$ or, $=10\sqrt{93} m/s $ or, $\approx 96.4 ft/s$
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