Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.12 - Modeling Variation - 1.12 Exercises - Page 128: 44

Answer

$(a)$ $F=k\frac{ws^2}{r}$ $(b)$ $s_2=48mi/h$

Work Step by Step

$(a)$ According to the information given in the problem, we can write the equation: $F=k\frac{ws^2}{r}$ Where $k$ is the constant of proportionality. $(b)$ For the first car: $F_1$ is unknown $w_1=1600 lb$ $s_1=60mi/h$ $k$ is unknown For the second car: $F_2$ is unknown $w_2=2500lb$ $s_2$ is unknown $F_1=F_2$ $F_1=\frac{k(1600)\times60^2}{r}$ $F_2=\frac{k(2500)\times {s_2}^2}{r}$ $\frac{k(1600)\times60^2}{r}=\frac{k(2500)\times {s_2}^2}{r}$ $k(1600)\times60^2=k(2500)\times {s_2}^2$ $2500{s_2}^2=1600\times60^2$ $25{s_2}^2=16\times3600$ ${s_2}^2=2304$ $s_2=48mi/h$
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