An airplane is flying at an altitude of 8 miles and passes over a radar station. When the airplane is 12 miles from the base of the station, the radar detects that its horizontal distance is changing at a rate of 320 mph. Find how fast the airplane is flying at this point in time.

The question asks to find the speed of the airplane. I know $\displaystyle speed = \frac{distance}{time}$. And, in this case, if I were to draw a right triangle with the radar station and airplane, I get the distance as $\sqrt{80}$ miles. How do I then find time? Do I even have to find time?

If it helps, the answer is 160 mph

  • $\begingroup$ Please show your work. $\endgroup$ – user114628 Feb 16 '14 at 9:04
  • $\begingroup$ Edited my question. I don't know how to use mathematical notation on the computer though $\endgroup$ – TheEconomist Feb 16 '14 at 9:08
  • $\begingroup$ @TheEconomist take a look at meta.math.stackexchange.com/q/5020/72616 $\endgroup$ – Justin Feb 16 '14 at 9:16
  • $\begingroup$ This is a really weird question. The airplane is not traveling up nor down. We are told that the airplane is traveling at a horizontal speed of 320 mph. So isn't the speed that the plane is traveling at 320 mph? $\endgroup$ – Justin Feb 16 '14 at 9:22
  • 1
    $\begingroup$ I think that the altitude and distance from station information yield no useful information. Focusing on the horizontal speed, the relative speed the radar detects will be $2h$ mph (as the radar pulse covers twice the distance), where $h$ is the horizontal speed of the aircraft. So $2h=320$, leading to $h=160$ mph. $\endgroup$ – Alijah Ahmed Feb 16 '14 at 10:19

This question is dumb

Answer is 238 mph


this question is bad because no life because no calculus

dx/dt = 320 dy/dt = 0 solve for change in hypotenuse

x^2 + y^2 = C^2 differentiate with respect to time

  • $\begingroup$ Please be more clear in oyur answer, this seems un related !!! $\endgroup$ – Nizar Dec 3 '15 at 10:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.