Calculus

posted by .

Two ships leave the same port at noon. Ship A sails north at 22 mph, and ship B sails east at 12 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.)

  • Calculus -

    after t hours, the distance d is given in terms of the distances x east and y north,

    d^2 = x^2 + y^2
    2d dd/dt = 2x dx/dt + 2y dy/dt

    at 1:00, x=12 and y=22, so
    d^2 = 12^2 + 22^2
    d = 25

    so,

    2*25 dd/dt = 2(12)(12) + 2(22)(22)
    dd/dt = 25.12 mi/hr

  • Calculus -

    QUESTION 3

    A boat sails 30 miles to the east from a point P, then it changes direction and sails to the south. If this boat is sailing at a constant speed of 10 miles/hr, at what rate is its distance from the point P increasing

    a) 2 hours after it leaves the point P
    b) 7 hours after it leaves the point P

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Trig

    A ship leaves its homeport and sails on a bearing of N28degrees10'E. Another ship leaves the same port at the same time and sails on a bearing of S61degrees50'E. If the first ship sails at 24.0 mph and second sails at 28mph, find the …
  2. Calculus

    at 12 noon ship A is 65 km due north of a second ship B. Ship A sails south at a rate of 14km/hr, and ship B sails west at a rate of 16km/hr. How fast are the two ships approaching each other 1.5 hours later at 1:30pm?
  3. math

    at 12 noon ship A is 65 km due north of a second ship B. Ship A sails south at a rate of 14km/hr, and ship B sails west at a rate of 16km/hr. How fast are the two ships approaching each other 1.5 hours later at 1:30pm?
  4. Trig

    Two ships leave the same port at 7.am. The first ship sails towards europe on a 54 degree course at a constant rate of 36 mi/h. The second ship,neither a tropical destination, sails on a 144 degree course at a constant speed of 42 …
  5. engineering science N4

    Two ships leave port simultaneously. Ship A sails north-west at 30 km/h and ship B sails S 40 degrees W at 30 km/h. Calculate the velocity of ship B relative to the velocity of ship A.
  6. math

    A ship leaves a port at 12:00 Noon and sails East at speed of 10 miles/hour. Another ship leaves the same port at 1:00 PM and sails North at a speed of 20 miles/hour. At what time are the two ships going to be 50 miles apart from each …
  7. calculus

    We know this is a piecewise function and we solved the first part, but we cannot figure out the other equation. A passenger ship leaves port sailing east at 16 mph. Two hours later, a cargo ship leaves the same port heading north at …
  8. Calculus

    At noon of a certain day,ship A is 60 km due north of ship B. If A sails east at 12 km/hr and B sails north 9 km/hr,determine how rapidly the distance between them is changing 2 hrs later. Is it increasing or decreasing?
  9. trigonometry

    A ship leaves its home port and sails on a bearing N38°15'E at 24 mph.At the same instant,another ship leaves the same port on a bearing S51°45'E at 28 mph.Find the distance between the two ships after 8 hours.
  10. Calculus

    Two ships leave the same port at noon. Ship A sails north at 12 mph, and ship B sails east at 19 mph. How fast is the distance between them changing at 1 p.m.?

More Similar Questions