Calculus I Related Rates:

An airplane is flying at an altitude of 5 miles and passes directly over a radar antenna (see figure). When the plane is 10 miles away (s = 10), the radar detects that the distance s is changing at a rate of 240 miles per hour. What is the speed of the plane?

Question

Mathematics

Araceli Murray

11 July, 15:51

Calculus I Related Rates:

An airplane is flying at an altitude of 5 miles and passes directly over a radar antenna (see figure). When the plane is 10 miles away (s = 10), the radar detects that the distance s is changing at a rate of 240 miles per hour. What is the speed of the plane?

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Answers (1)

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Matthew Jennings · Answer 1

Let s be the hypotenuse and using the Pythgorean theorem,

s2 = 25 + x2 taking the first derivative of the function with respect to t, the result is 2s ds / dt = 2x dx / dt substituting s = 10 and ds/dt = 240,

we get x = sqrt (100-25) = 5 √3

Calculus I Related Rates:An airplane is flying at an altitude of 5 miles and passes directly over a radar antenna (see figure). When the plane is 10 miles away (s = 10), the radar detects that the distance s is changing at a rate of 240 miles per hour. What is the speed of the plane?

Calculus I Related Rates:

An airplane is flying at an altitude of 5 miles and passes directly over a radar antenna (see figure). When the plane is 10 miles away (s = 10), the radar detects that the distance s is changing at a rate of 240 miles per hour. What is the speed of the plane?