Expert: Paul Klarreich - 2/11/2010

Question
I know how to set up most related rate problems, but this one doesn't make any sense to me. I can do the kind where a ladder is sliding away from a wall, dirt is falling onto a pile etc. But this one doesn't make sense to me. I can't find any similar examples in my text book either.

An airplane is flying towards a radar station at a constant height of 6km above the ground. If the distance (s) between the airplane and the radar station is decreasing at a rate of 400 km/hr when s=10 km, what is the horizontal speed of the plane?

Answer
Questioner: Christina
Country: United States
Category: Calculus
Private: No
Subject: Airplane related rates
Question: I know how to set up most related rate problems, but this one doesn't make any sense to me. I can do the kind where a ladder is sliding away from a wall, dirt is falling onto a pile etc. But this one doesn't make sense to me. I can't find any similar examples in my text book either.

An airplane is flying towards a radar station at a constant height of 6km above the ground.

>>>  So y = 6, a constant.

If the distance (s) between the airplane and the radar station is decreasing at a rate of 400 km/hr

>>> So  ds/dt = -400

when s=10 km, what is the horizontal speed of the plane?

>>> So you must find  dx/dt



      /|
     / |
    /  |
 s /   |  6
  /    |
 /     |
/      |
/       |
--------|
  x

ds/dt = - 400
Find dx/dt, when  s = 10

Relation:

x^2 + 6^2 = s^2

Take it from there.