Calculus

Ship A is moving east at 20 miles per hour, while ship B is moving north at 15 miles per hour. At noon ship A was 5 miles east of an island, and ship B was 75 miles south of the island.
At what rate is the distance of the ships changing at 1 pm?

  1. 👍
  2. 👎
  3. 👁
  1. x = 5 + 20 t
    y = -75 + 15 t
    z =distance =sqrt(25+5625)
    (I bet you meant 7.5 miles but oh well)

    dx/dt = 20
    dy/dt = 15

    at t = 0 x = 5 and y = -75
    z^2 = x^2 + y^2
    2 z dz = 2x dx + 2 y dy
    so
    dz = (x dx + y dy)/z
    and dz/dt = (x dx/dt + ydy/dt)/z
    = (5*20-75*15)/sqrt(25+56250

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 22 knots. How fast (in knots) is the distance between the ships changing at 7 PM? (Note: 1 knot is a speed

  2. math

    At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 23 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed

  3. Calculus

    At noon, ship A is 180 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing north at 30 km/h. How fast is the distance between the ships changing at 4:00 PM?

  4. Calculus

    At noon, ship A is 130 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?

  1. CALCULUS

    At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 23 knots and ship B is sailing north at 19 knots. How fast (in knots) is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed

  2. calc

    At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 30 km/h. How fast is the distance between the ships changing at 4:00 PM?

  3. Calculus

    At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h, and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 P.M.?

  4. calculus

    At noon, ship A is 20 kilometers north of Ship B. Ship A is traveling south at 50 kilometers per hour, and ship B is traveling east at 40 kilometers per hour. If visibility is 10 kilometers, could the people on the two ships ever

  1. precalulus

    a ship travels 60 miles due east, then adjusts its course northward. after travelling 80 miles in the new direction, the ship is 139 miles from its point of departure. calculate the ship's bearing.

  2. Calculus

    At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing at 7 PM? (Note: 1 knot is a speed

  3. Math!

    At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 25 knots and ship B is sailing north at 16 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed

  4. calculus

    At noon, ship A is 110 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?

You can view more similar questions or ask a new question.