Kelvin M.
asked • 30dCalculus homework question
Two cars leave from the same location at exactly 8:00am if cat A is driving directly north at 60 miles per hour and car B is driving directly east at 25 miles per hour determine the rate that the distance between the cars is changing at 10:00am
2 Answers By Expert Tutors
At moment t distance d between cars d^{2} = (60t)^{2} + (25t)^{2}= 4225t^{2}.
So, d = 65t. Then rate of change of distance is derivative d' = 65 mi/h is constant. And because at 10:00 AM d' = 65 mi/h
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 a= 60 mph North




L__________> b= 25 mph East
If you're going to look at the figure above, the rate that we are looking for is the hypotenuse of a right triangle. From 8am to 10am is 2 hours.
So let say:
c = rate of the distance between the car is changing.
Using the Pythagorean Theorem.
c^{2} = a^{2}+b^{2}
c^{2} = (60)^{2}+(25)^{2}
c =√(3600+625)
c = 65 miles per hour.
The 2 hours doesn't matter because the rate is still going to be the same in any time. However, if you are looking for the distance after 2 hours, that would be (65)(2) = 130 miles.
65 miles per hour is basically the same as 130 miles in 2 hours.
Tom K.
29d
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Rohit M.
130 miles30d