The problem given in my book is:(adsbygoogle = window.adsbygoogle || []).push({});

I set up and solved the problem this way: A plane flying horizontally at an altitude of 1mi and a speed of 500 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2mi away from the station.

dx/dt= 500 mi/h

x = 2mi

y = 1mi (constant)

Distance:

s^{2}= y^{2}+ x^{2}

s^{2}= 1 + x^{2}

s = (1 + x^{2})^{1/2}

d/dt=d/dt[sqrt(1 + x^{2})^{1/2}]

ds/dt= (1/2)(1 + x^{2})^{-1/2}* (2x(dx/dt))

ds/dt= (1 + x^{2})^{-1/2}* (x(dx/dt))

ds/dt= [tex]\frac{x(dx/dt)}{(1 + x^2)^{1/2}}[/tex]

Substiting:

ds/dt= [tex]\frac{(2)(500)}{(1 + (2)^2)^{1/2}}[/tex]

ds/dt= [tex]\frac{1000}{\sqrt{5}}[/tex]

The final answer:

ds/dt= [tex]200\sqrt{5}[/tex] mi/h

However the back of my book has: [tex]250\sqrt{3}[/tex] mi/h

What am I doing wrong?

Thank you,

-GM-

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# Homework Help: Related Rates - Not getting answer in book

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