Answer to Question #177540 in Calculus for kienth bryan doroin

Question #177540

Starting from the same point, Biden starts walking eastward at 52 m/s while Trump starts running towards the south at 86 m/s. How fast is the distance between Biden and Trump increasing after 2 seconds?


1
Expert's answer
2021-04-15T07:19:33-0400

"let\\ x\\ represent\\ Biden's\\ distance\\ from\\ the\\ origin\\ point"

"\\ \\ \\ \\ \\ \\ y\\ represent\\ Trump's\\ distance\\ from\\ the\\ origin\\ point"

"\\ \\ \\ \\ \\ \\ t\\ represent\\ the\\ time\\ after\\ they\\ started\\ walking"

"\\ \\ \\ \\ \\ z\\ represent\\ the\\ distance\\ between\\ them"

"z=\\ \\sqrt{x^2+y^2}"

"\\frac{dx}{dt}=52"

"\\frac{dy}{dt}=86"

"we\\ wish\\ to\\ calculate\\frac{dz}{dt}"

"\\int{\\frac{dx}{dt}dt}=52t+c"

"\\int{\\frac{dy}{dt}dt}=86t+k"

"at\\ t=0,\\"

"x=0,\\ y=0"

"52\\left(0\\right)+c=0\\rightarrow c=0\\rightarrow x=52t"

"86\\left(0\\right)+k=0\\rightarrow k=0\\rightarrow y=86t"

"z=\\sqrt{x^2+y^2}=\\ \\sqrt{\\left(52t\\right)^2+\\left(86t\\right)^2}=\\ \\sqrt{10100}\\ t"

"\\frac{dz}{dt}=\\ \\sqrt{10100}=100.499m\/s"


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