anonymous
  • anonymous
Related rates An aircraft is 8 km above the ground and flying horizontally at a speed of 400 km/h. How far is the distance between the aircraft and the radio beacon increasing 3 minutes after the aircraft passes directly over the beacon? could someone please explain.
OCW Scholar - Single Variable Calculus
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
"How far is the distance between the aircraft and the radio beacon increasing 3 minutes after the aircraft passes directly over the beacon?" do you mean how fast instead of how far? If so than the solution is as follows: Let the height the plane is flying at be h = 8 km. Let the distance it has traveled along the ground (that is, perfectly horizontally) be x. Then dx/dt = 400 km/h. Call the distance between the plane and the radio beacon L. Then h, x, and L form a right triangle. By the Pythagorean Theorem, \[L ^{2}=x^{2}+h^{2}\] So\[L=\sqrt{x^2+h^2}\] now we differentiate with respect to time, \[dL/dt=(x/\sqrt{x^2+h^2})dx/dt\] After 3 minutes the aircraft has gone (horizontally) (3 min)x(400 km/h) = (0.05 h)x(400 km/h) = 20 km. Plug in x = 20 km, h = 8 km and dx/dt = 400 km/h and you get dL/dt = 371.39 km/h, which is about 103.15 m/sec. Note: if you're having trouble following, draw a picture and you'll see what I'm talking about.

Looking for something else?

Not the answer you are looking for? Search for more explanations.