SOLUTION: An air traffic controller spots two planes flying at the same altitude. Their flight paths form a right angle at point P. One plane is 150 miles from point P and is moving at 460 m

Question 1202670: An air traffic controller spots two planes flying at the same altitude. Their flight paths form a right angle at point P. One plane is 150 miles from point P and is moving at 460 miles per hour. The other plane is 200 miles from point P and is moving at 460 miles per hour. Write the distance s between the planes as a function of time t.
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Imagine the two planes are moving towards P
The two places are at right angles to each other. ( In same Plane)

Form two equations that shows the position of each plane.
Plane A position at any time = 150 - 450t
Place B position = 200 - 450t perpendicular
The d istance between tem will be hypotenuse of the triangle with sides that are given by Plane A & B positions
c^2= a^2 + b^2 (Pythagoras Theorem)

c(t)^2 = (150t- 450)^2 +(200t-450)^2
22500t2-135000202500 +40000t^2-180000+202500
simplify to get the required function

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
An air traffic controller spots two planes flying at the same altitude. Their flight paths form a right angle at point P.
One plane is 150 miles from point P and is moving at 460 miles per hour.
The other plane is 200 miles from point P and is moving at 460 miles per hour.
Write the distance s between the planes as a function of time t.
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The problem formulation is DEFECTIVE, because it does not define PRECISELY the direction of the planes flights.

They can move from point P or to point P (there are four different possible combinations).

Therefore, any attempts to solve the problem are non-sensical - until the problem is posed in a right way.

Lowest possible score to the composer of this problem for his unsatisfactory job.

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