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# Last Math Question

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I need helo on a VERY hard question (for me I guess)

John threw a ball straight up in the air at 30 meters per second, how far did it go up in 10 seconds?

PsychoBaker  Jun 17, 2017
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$$v_o=30\\ x_0=0\\ \ddot{x}=-9.8\\ \dot{x}=-9.8t+k_1\\ when\;\;t=0,\;\;\dot{x}=30\;\;so\;\;k_1=30\\ \dot{x}=-9.8t+30\\ x=\frac{-9.8t^2}{2}+30t+k_2\\ when\;\;t=0,\;\;x=0\;\;so\;\;k_2=0\\ x=-4.9t^2+30t\\~\\ Max\;\;reached \;\;when\;\;\dot{x}=0\\ \dot{x}=-9.8t+30=0\\ t=30/9.8\approx3.06sec\\ When\;\;t=3.06sec\\ x=-4.9*3.06^2+30*3.06\\ x\approx 45.9\;metres$$

I have not checked this fro errors but the method is correct :)

Melody  Jun 17, 2017