ahmadu university zaria nigeria

posted by .

Ship A is sailing due south at 25 km/hr. At the same time, a second ship B, 50km miles south of A, is sailing due east at 20 km/hr.
(a) at what rate are they approaching or separating at the end of one hour?
(b) At what rate are they approaching or separating at the end of two hours?
(c) When do they cease to approach each other and how far apart are they at that instant

  • calculus -

    Let B start at (0,0). Then the positions of the boats at time t are
    A(t) = (0,50-25t)
    B(t) = (20t,0)
    and the distance d is thus
    d^2 = (20t)^2 + (50-25t)^2
    = 1025t^2 - 2500t + 2500
    2d dd/dt = 2050t - 2500

    At t=1, d ~= 32
    64 dd/dt = 2050-2500
    dd/dt = -7.03 km/hr

    At t=2, d = 40
    80 dd/dt = 4100-2500
    dd/dt = +20

    dd/dt=0 when t=1.22 so d = 31.23

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Optimization At 1:00 PM ship A is 30 miles due south of ship B and is sailing north at a rate of 15mph. If ship B is sailing due west at a rate of 10mph, at what time will the distance between the two ships be minimal?
  2. Calculus

    one ship (A) is sailing due south at 16 miles per hour and a second ship (B), 32 miles south of A, is sailing due east at 12 miles per hour. At what rate are they approaching at the end of 1 hour?
  3. calculus

    At noon, ship A starts sailing due east at the rate of 20km/hr. Ath the time, ship B, which is located 100km east of ship A initially, starts sailing on a course 60 degrees north of west at the rate of 10km/hr. How fast is the distance …
  4. Calculus

    At 1:00 p.m. ship A is 25 km due north of ship B. If ship A is sailing west at a rate of 16km/h and ship B is sailing south at 20km/h, find the rate at which the distance between the two ships is changing at 1:30 p.m.
  5. calculus

    At 1:00 p.m. ship A is 25 km due north of ship B. If ship A is sailing west at a rate of 16km/h and ship B is sailing south at 20km/h What is the first time after 3:00 p.m. that the hands of the clock are together?
  6. Calculus

    At 4 PM ship A is 40 miles due South Ship B. Ship A is sailing due South at a rate of 20 knots while ship B is sailing due East at a rate of 25 knots. Find the rate of change of the distance between the ships at 3 PM and at 5 PM. At …
  7. calculus

    At 9am, ship B was 65 miles due east of another ship, A. Ship B was then sailing due west at 10 miles per hour, and A was sailing due south at 15 miles per hour. If they continue their respective courses, when will they be nearest …
  8. Differential Calculus

    At 9am ship B is 65 miles due east of another ship A. Ship B is then sailing due west at 10mi/h and A is sailing due south at 15 mi/hr if they continue in their respective course when will they be nearest to one another?
  9. CALCULUS!!!!!

    At 9am, ship B was 65 miles due east of another ship, A. Ship B was then sailing due west at 10 miles per hour, and A was sailing due south at 15 miles per hour. If they continue their respective courses, when will they be nearest …
  10. AP Calculus

    Ship A is sailing due west at 8km/hr when it sees ship B northwest of its present position. If ship B is sailing due south at 3km/hr, then how close will they come on their courses?

More Similar Questions