# related rates airplane expample.

#### mags22

##### New member
An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane is 10 miles away (s = 10), the radar detects that the distance s is changing at a rate of 240 miles per hour. What is the speed of the airplane?

#### mmm4444bot

##### Super Moderator
Staff member

Hello. Are far did you get? Please explain where you're stuck. Thank you!

#### HallsofIvy

##### Elite Member
You did not say what "distance s" means! Is it the distance between the airplane and the radar antenna? If so, since the antenna is fixed on the ground, isn't the ground speed of the airplane exactly what the radar is giving?

#### Dr.Peterson

##### Elite Member
You did not say what "distance s" means! Is it the distance between the airplane and the radar antenna? If so, since the antenna is fixed on the ground, isn't the ground speed of the airplane exactly what the radar is giving?
No, I think it's like this:

We know ds/dt, we want dx/dt.

@mags22, what ideas have you had? Can you write an equation relating x and s?

#### HallsofIvy

##### Elite Member
Ouch! I completely missed the altitude! Thanks, Dr. Peterson.