Answer to Question #264049 in Calculus for Lou

Question #264049

A billiard ball is hit and travels in a straight line. If 𝑠 π‘π‘š is the distance of the ball from

its initial position at 𝑑 𝑠𝑒𝑐, then 𝑠 = 100𝑑2 + 100𝑑. If the ball hits the cushion that is 39 π‘π‘š from its

initial position, at what velocity does it hit the cushion?Β 


1
Expert's answer
2021-11-11T12:26:38-0500

Given:

"s(t) =100 t^{2}+100 t \\\\\ns=39 \\mathrm{~cm} . \\\\\n\\Rightarrow 39=100 t^{2}+100 t \\\\\n\\Rightarrow 100 t^{2}+100 t-39=0 \\\\\n\\Rightarrow \\frac{-100 \\pm \\sqrt{(100)^{2}-4(-39)(100)}}{2(100)} \\\\\n\\Rightarrow \\frac{-100 \\pm \\sqrt{10000+15600}}{200} \\\\\n=\\frac{-100 \\pm 160}{200} \\\\\n=\\frac{-100+160}{200} \\ [\\text{t can not be negative}] \\\\ \n=\\frac{60}{200}=\\frac{3}{10}"

Velocity "(t)=\\frac{d}{dt}[100t^2+100t]=200t+100\\\\"

At "t=\\frac{3}{10}"

Velocity "=" "200(\\frac{3}{10})+100=160\\ cm\/s"


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