Posted by **David** on Sunday, September 9, 2012 at 11:53am.

an air traffic controller spots two planes at the same altitude flying towards one another. their flight paths form a right angle at point p. One plane is 150 miles from point p and is moving 450mph. the other plane is moving at 450mph but is 200 miles from point p. write the distance d between the planes as a function of time t.

- Math -
**Steve**, Sunday, September 9, 2012 at 2:19pm
the planes' distances from p form a scaled-up 3-4-5 right triangle, so at the time specified, d, the hypotenuse, is 250

at time t hours later,

d^2 = (150-450t)^2 + (200-450t)^2

That's kind of nasty, so a simpler formula would be,

Let x be the distance of the first plane. Then the second plane is 4/3 x away from p.

d^2 = x^2 + (4/3 x)^2 = 25/9 x^2

since x = 150-250t,

d^2 = 25/9 (150-450t)^2

= 25/9 * 150^2 (1-3t)^2

= 25*2500 (1-3t)^2

## Answer this Question

## Related Questions

- Math - an air traffic controller spots two planes at the same altitude flying ...
- 11th grade-Math! - an air traffic controller spots two planes at the same ...
- Precalculus - an air traffic controller spots two planes at the same altitude ...
- Calculus - An air traffic controller spots 2 planes at the same altitude ...
- Pre Calc - A plane (A) heading south at 120 mph and a plane (B) heading west at ...
- Calc - Two commercial airplanes are flying at an altitude of 40,000 ft along ...
- Calc - Two commercial airplanes are flying at an altitude of 40,000 ft along ...
- calculus - Two commercial airplanes are flying at an altitude of 40,000 ft ...
- Math - Two Planes leave an airport at the same time, one flying 300km/h and the ...
- Physics - A flight traffic controller is watching two planes. One is 20.0 km ...

More Related Questions