Question

I'm doing the final exam and need help setting up problem #6:

6. A highway patrol plane is flying 1 mile above a long, straight road, with constant
ground speed of 120 m.p.h. Using radar, the pilot detects a car whose distance
from the plane is 1.5 miles and decreasing at a rate of 136 m.p.h. How fast is the
car traveling along the highway? (Hint: You may give an exact answer, or use the
fact that
√
5 ≈ 2.2.)

Answer 1

Here is my work on my paper so far...but just don't know how to proceed.

Answer 2

I worked out the problem and this is the setup I used. Can you please tell me the answer you found so I can also know if I approached this correctly.

Answer 3

Hey, yes, I eventually think I figured this out. I set up the same as you and then did implicit differentiation. My final answer was 182.5 mph. Did you find a similar result?

Answer 4

Not exactly, in my case 182.5mph was the combined rate of the plane and the car together. So, the value of x in my diagram decreases at 182.5mph. 120mph of this decrease is contributed by the plane so i got a rate of 62.5mph for the car.

Answer 5

Yes, very good point! I was wondering if mine was right because it didn't seem to be realistic. Thanks for your input!