related rate word problem: plane and radar station

riocean17

New member
Joined
Jan 25, 2007
Messages
3
A plane flying parallel to the ground at a height of 4 km passes over a radar station. A short time later, the radar equipment reveals that the plane is 5 km away and that the distance between the plane and the station is increasing at a rate of 300 km per hour. At that moment, how fast is the plane moving horizontally?

I drew a picture of a right triangle and labeled the appropriate legs. I know that, at that time, the plane and the radar station are 5 km apart. I also know that D = RT ("distance equals rate times time").

Our teacher told us to use derivatives, but I can't figure out how to complete the problem or the equation to use to even find a derivative. I just need help getting started and the equation or formula to use.
 
did you make a sketch? graph and connect these 3 points with line segments.

A ... radar station
B ... point 4 km directly overhead the radar station
C ... airplane position

see the right triangle formed by the points?

vertical leg, AB = 4 km
horizontal leg, BC = x
hypotenuse, AC = z

using Pythagoras ...

z<sup>2</sup> = x<sup>2</sup> + 4<sup>2</sup>

take the derivative of the above equation w/r to time, then substitute your given and derived information. solve for dx/dt (airplane speed). you have all the necessary information, so do it.
 
Top