Posted by **becca** on Tuesday, January 17, 2012 at 12:29am.

An airplane flying west at 300 miles per hour goes over the control tower at noon, and a second airplane at the same altitude, flying north at 400 miles per hour, goes over the tower an hour later. How fast is the distance between the airplanes changing at 2:00 P.M.?

- calculus -
**Steve**, Tuesday, January 17, 2012 at 2:41pm
Draw a diagram

Let the tower be at (0,0)

plane A is at distance a = 300t West after t hours

Plane B is at position b = 400(t-1) North after t hours, counting from 12:00

The distance d between the planes is given by

d^2 = (300t)^2 + (400(t-1))^2

2d dd/dt = 2(300t)(300) + 2(400(t-1))(400)

at 2:00, t=2, so

d = 200√13

400√13 dd/dt = 360000 + 320000 = 680000

dd/dt = 6800/4√13 = 1700/√13 = 471.5

feel free to check my math...

## Answer This Question

## Related Questions

- Calculus - Derivatives - chain rule An airplane, flying horizontally at an ...
- Calculus - Derivatives - chain rule An airplane, flying horizontally at an ...
- Trigonometry- Help! - After one hour in flight, an airplane is located 200 miles...
- math - A helicopter is 400 miles directly north of Ghana and is flying at 20 ...
- calculus - an airplane is flying at an altitude of 6.7 miles towards a point ...
- Math - Two airplanes at 25,000 ft above the ground are flying toward the same ...
- math - two airplanes left the same airport traveling in opposite direction. if ...
- math - An airplane leaves Atlanta at 2 PM and flies north at 250 miles per hour...
- Math Calculus 2 - At a certain instant an aircraft flying due east at 240 miles ...
- Calculus - An airplane is flying in still air with an airspeed of 325 miles per ...

More Related Questions