A road running north to south crosses a road going east to west at the point P. Car A is driving north along the first road, and an airplane is flying east above the second road. At a particular time the car is 15 kilometers to the north of P and traveling at 55 km/hr, while the airplane is flying at speed 175 km/hr 10 kilometers east of P at an altitude of 2 km. How fast is the distance between the car and the airplane changing?

Would you use the derivative of the pathagorium theorem? How would you go about doing this?

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  1. D^2 = Pn^2 + Pe^2 + 2^2

    use implicit differentiation ... 2 D dD/dt = 2 Pn dPn/dt + 2 Pe dPe/dt

    √(15^2 + 10^2 + 2^2) dD/dt = 15 * 55 + 10 * 175

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  2. But when I did this, I got 141.96 which according to the database I'm entering this into, Is still incorrect.

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  3. 141.96 may have too many significant figures

    try rounding to three digits

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