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# Answer to Question #230353 in Civil and Environmental Engineering for syra

Question #230353
A stone is thrown downward with an initial velocity of 5m/s from a 20-meter high building. Find the time it takes to reach the ground.
1
2021-08-31T01:42:55-0400

"h= ut + \\frac{1}{2}gt^2\\\\\n20= 5t + \\frac{1}{2}*9.8*t^2\\\\\n\\mathrm{Multiply\\:both\\:sides\\:by\\:}10\\\\\n20\\cdot \\:10=5t\\cdot \\:10+\\frac{1}{2}\\cdot \\:9.8t^2\\cdot \\:10\\\\\n50t+49t^2=200\\\\\n\\mathrm{Subtract\\:}200\\mathrm{\\:from\\:both\\:sides}\\\\\n50t+49t^2-200=200-200\\\\\n\\mathrm{Simplify}\\\\\n49t^2+50t-200=0\\\\\nt_{1,\\:2}=\\frac{-50\\pm \\sqrt{50^2-4\\cdot \\:49\\left(-200\\right)}}{2\\cdot \\:49}\\\\\nt_1=\\frac{-50+10\\sqrt{417}}{2\\cdot \\:49},\\:t_2=\\frac{-50-10\\sqrt{417}}{2\\cdot \\:49}\\\\\nt=\\frac{5\\left(\\sqrt{417}-5\\right)}{49},\\:t=-\\frac{5\\left(5+\\sqrt{417}\\right)}{49}\\\\\nt=1.57352 s"

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