Hello, If you are solving this can you show in boring details I want to get this

Question

Hello, If you are solving this can you show in boring details I want to get this one excatly.Thank you

Question 1: You are a prisoner trying to escape your unjust captivity. You run toward the last barrier between you and freedom, a 20 ft. barbed wire fence. Your speed is 5 ft./sec. Liberty is close. With each step you feel lighter, more human. However, in the depths of reve problem and that you must find how quickly the distance between you and the top of the fence is changing. For the purposes of this problem suppose your height is 0 ft lry, a mere 50 ft. from the fence, you re alize vou are in a related rates the purposes of this problem suppose yo

Explanation / Answer

height of the fence = 20 ft

let us say you are at a horizontal distance x ft from fence

by right angle triangle, hypotenuse , you get the distance between you and top of the fence . say it is y

then y^2 = x^2 +20^2

differentiate the equation with respect to time

2 *y dy/dt = 2x*dx/dt

we need to find dy/dt when x= 50 and dx/dt =v= 5ft/sec

when x= 50 , y= sqrt(50^2+20^2) = 10 *sqrt(29)

so , 2 * 10*sqrt(29) *dy/dt = 2*50*5

dy/dt = 25/sqrt(29) = 4.64 ft/sec -------ANSWER

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