What is the rate of change?
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| Question Part |
| Submissions Used |
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 120 miles from the point and has a speed of 360 miles per hour. The other is 160 miles from the point and has a speed of 480 miles per hour.
Part (a)
At what rate is the distance between the planes changing?
Step 1 of 5
Let s denote the distance in miles as shown in the following figure. The origin represents the point of convergence.
The distance s between the planes is given by the formula,
s =
| [img src=”http://www.webassign.net/wastatic/wacache1ff8a7b5dc7a7d1f0ed65aaa29c04b1e/watex/img/sqrt2a.gif” > | x2 + y2 |
.
Thus,
s2 = x2 + y2.
One plane is 120 miles away and moving towards the point of convergence at 360 miles per hour so x = 120and
| dx |
| dt |
= − 
.
The other plane is 160 miles away and moving towards the point of convergence at 480 miles per hour, so y= 160 and
| dy |
| dt |
= − .
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