calculus

posted by .

a man on a dock is pulling in a boat by means of a rope attached to the bow of the boat 1ft above the water level and passing through a simple pulley located on a dock 8ft above the water level. if he pulls in the rope at a rate of 2ft/sec, how fast is the boat approaching the dock when the bow of the boat is 24ft from the point that is directly below the pulley?

  • calculus -

    consider y=0 at the bot bow, so the pulley is at height 7

    if the boat is at distance x, the length r of the rope from pulley to boat, is given by

    r^2 = x^2 + 7^2
    when x=24, r=25
    dr/dt = -2

    2r dr/dt = 2x dx/dt
    2(25)(-2) = 2(24) dx/dt

    dx/dt = -25/12 ft/s

  • calculus -

    how ambiguous a way to present the problem

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching …
  2. Calculus

    A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1.4 m/s, how fast is the boat approaching …
  3. calculus

    A boat is pulled into a dock by a string attached to the bow of the boat and passing through a pulley on the dock that is1ft higher than the bow of the boat. If the string is pulled at a rate of 3 ft/second, how fast is the boat approaching …
  4. calculus

    A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1.4 m/s, how fast is the boat approaching …
  5. calculus

    A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching …
  6. Calculus

    A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching …
  7. Calculus Practice Problems

    A boat is pulled into a dock by a rope attached to the bow (front end) of the boat and passing through a pulley on the dock that is 4 m higher than the bow of the boat. If the rope is pulled in at a rate of 3 m/s, at what speed is …
  8. Calculus

    A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1m/s,how fast is the boat approaching …
  9. calc 1

    A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching …
  10. Calculus

    A man on a wharf is pulling in a boat by means of a rope attached to the bow of the boat 1 meter above water level and passing through a simple pulley located on the dock 8 meters above water level. If he pulls in the rope at the rate …

More Similar Questions