AP CALC

posted by .

Two roads intersect at right angles. At a certain moment, one bicyclist is 8 miles due NORTH of the intersection traveling TOWARDS the intersection at a rate of 16 miles/hour. A second bicyclist is 10 miles due WEST of the intersection traveling AWAY from the intersection at 12 miles/hour.
(a) How fast is distance between the two bicyclists changing at this moment?

  • AP CALC -

    make a diagram, let the distance the north biker is from the intersection be y miles, let the distance the west biker is from the intersection be x miles
    Let the distance between them be D
    D^2 = x^2 + y^2
    2D dD/dt = 2x dx/dt + 2y dy/dt

    given:
    dx/dt = 12 mph
    dy/dt = -16 mph (y is decreasing)
    find dD/dt when x=10 and y=8
    then D^2 = 100+64
    D = √164

    dD/dt =(2(10)(12) + 2(8)(-16))/(2√164) = .....

    you finish the arithmetic

  • AP CALC -

    My final answer was -8/square root of 164. Is that correct?

  • AP CALC -

    I believe the correct answer is 0.635 but i got 0.625.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Cameron is located 2 miles due East of an intersection between two country roads. He decides to walk in a straight line (cross-country) toward a position 3 miles due North of the intersection; it takes Cameron one hour to reach that …
  2. calculus

    Two commercial airplanes are flying at an altitude of 40,000 ft along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 429 knots (nautical miles per hour; a nautical …
  3. FREE BODY DIAGRAM calculus

    A car is traveling north towards an intersection at 60mph at the same time a truck is headed east toward the same intersection at 45mph. Find the rate of change of the distance between the car and truck when the car is 3 miles south …
  4. Calculus

    One ship is 20 miles due North of another ship, and is sailing South at the rate of 10 miles per hour. The second ship sails West at the rate of 20 miles per hour. For how long will the ships continue to approach each other?
  5. Calc

    Two commercial airplanes are flying at an altitude of 40,000 ft along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 427 knots (nautical miles per hour; a nautical …
  6. Calc

    Two commercial airplanes are flying at an altitude of 40,000 ft along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 427 knots (nautical miles per hour; a nautical …
  7. Calculus

    Suppose that two boats leave a dock at different times. One heads due north, the other due east. Find the rate at which the distance between the boats is changing when the first boat is 56 miles from the dock traveling at a speed of …
  8. Math

    A surfer drives his dune buggy out into the sand dunes.He follows his compass 10 miles due north and then turns due west. If he ends up approximately 35 miles from where he started how far west did he travel?
  9. Calc 1

    Related Rates: Two cars approach the intersection of two highways. The one coming from the west is traveling at 60mph and the one traveling from north is traveling at 50 mph. At what rate is the distance between the cars changing when …
  10. calculus

    One bicycle is east of an intersection , and it is travelling towards the intersection of 9 miles per hour. at the same time a second bicycle is south of the intersection , and it is travelling away from the intersection at the rate …

More Similar Questions