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An airplane is flying an altitude of 5 miles and passes directly over a radar antenna. When the plane is 10 miles past the antenna, the rate at which the distance between the antenna and the plane is changing is 240 miles per hour. What is the speed of the plane?

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An airplane is flying an altitude of 5 miles and passes directly over a radar antenna.  When the plane is 10 miles past the antenna, the rate at which the distance between the antenna and the plane is changing is 240 miles per hour.  What is the speed of the plane?

precal · Answer

I have no idea how to set up this problem at all

precal · Answer

|dw:1407422113682:dw|

precal · Answer

Is this just a right triangle problem?

anonymous · Answer

|dw:1407422131885:dw|You have the equation
$$x^2+y^2=z^2$$

anonymous · Answer

Yes it is

precal · Answer

so they want dx/dt?

anonymous · Answer

When you differentiate implicitly, you're given that $\dfrac{dz}{dt}=240$ and $\dfrac{dy}{dt}=0$ because the plane doesn't change altitude. Solve for $\dfrac{dx}{dt}$.

precal · Answer

ok see you are working your magic again.......got it

anonymous · Answer

:)