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mestny [16]
2 years ago
15

Two airplanes are flying in the air at the same height. Airplane A is flying east at 300mi/h and airplane B is flying north at 2

00mi/h. If they are both heading to the same airport, located 90 miles east of airplane A and 120 miles north of airplane B, at what rate is the distance between the airplanes changing
Mathematics
1 answer:
Ipatiy [6.2K]2 years ago
6 0

Answer:

\frac{dAB}{dt}=340 mil/h

Step-by-step explanation:

The change of distance over time of the plain A is 300 mi/hour and 200 mi/hour for plane B. O is the point of the airport.

So, the distance from A to O AO = 90 miles and BO = 120 miles.

Now, we have a right triangle here.  We can use the Pythagorean theorem, so the distance between the planes will be:

AB^{2} =AO^{2}+BO^{2} (1)

AB =\sqrt{AO^{2}+BO^{2}}=

AB =\sqrt{90^{2}+120^{2}}=150 miles

If we take the derivative of the equation (1) we could find the change of the distance between planes.

2AB\frac{dAB}{dt}=2AO\frac{dAO}{dt}+2BO\frac{dBO}{dt}

2*150\frac{dAB}{dt}=2*90*300+2*120*200=102000 mil/h

\frac{dAB}{dt}=\frac{102000}{150*2}

Finally,

\frac{dAB}{dt}=340 mil/h

I hope it helps you!

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