calculus

posted by .

A plane flies horizontally with a speed Of 600km/h at an altitude of 10km and pasess directly over th town of quinton .find the rate at which the distance from the plane to quinton is increasing when its 20km away from quinton ?

  • calculus -

    let the horizontal distance from Quinton be x km
    let the distance between plane and Quinto by y km

    x^2 + 10^2 = y^2
    2x dx/dt = 2y dy/dt
    dy/dt = (x dx/dt)/y

    when x=20
    y^2 = 400 + 100 = 500
    y = √500 = 10√5
    dx/dt = 600 km/h
    dy/dt = 20(600)/10√5 = appr. 536.7 km/h

  • calculus -

    But did u use pythagoram theorom an how did u manipulate it ? And thanks because the answer is right .

  • calculus -

    yes, you can see in my first line of the solution that I used the Pythagorean theorem.
    I then differentiate with respect to time, since we were talking about "rates" in the question and I saw a rate given as 600 km/h

  • calculus -

    Thank you !

  • calculus -

    how did you get dy/dt to be (x dx/dt)/y

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calc

    A plane flying horizontally at an altitude of 1 mi and a speed of 510 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 6 mi away from the station. …
  2. Cal

    A plane flying horizontally at an altitude of 3 mi and a speed of 480 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 6 mi away from the station. …
  3. Calculus

    A plane flies horizontally with a speed Of 600km/h at an altitude of 10km and pasess directly over th town of quinton .find the rate at which the distance from the plane to quinton is increasing when its 20km away from quinton ?
  4. A plane flies horizontally at an altitude of 5 km

    A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is π/3, this angle is decreasing at a rate of π/4 rad/min. How fast is the plane traveling …
  5. calculus

    a plane flying horizontally at an altitude of 2 mi and a speed of 460 mi/h passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station.
  6. calculus

    A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station. …
  7. calculus

    A plane flying horizontally at an altitude of 1 mi and a speed of 560 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station. …
  8. Calculus

    A plane flying horizontally at an altitude of 2 mi and a speed of 420 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station.
  9. Calc

    A plane flying horizontally at an altitude of 2 mi and a speed of 420 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station.
  10. Calculus

    Someone had helped me yesterday, but I need it broken down more because I honestly don't understand any of this?

More Similar Questions