Post a New Question

Calculus

posted by .

a) A boat is pulled into a dock by a rope attached to the bow ("front") of the boat and passing through a pulley on the dock that is 1m 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 the dock when it is 8m from the dock?

b)A particle is moving along the curve y=√x. As the particle passes through the point (4,2), its x-coordinate increases at a rate of 3cm/s. How fast is the distance from the particle to the origin changing at this instant?

c)The price (in dollars) p and the quantity demanded q are related by the equation: p2+2q2=1100.
If R is revenue, dR/dt can be expressed by the following equation: dR/dt=A(dp/dt),
where A is a function of just q.
i)Find A.
ii)Find dR/dt when q=20 and dp/dt=4.

  • Calculus -

    If the boat is x meters from the dock, then the length of rope is given by

    r^2 = x^2 + 1
    2r r' = 2x x' = 2(8)(-1)
    rr' = -8

    So, r(8) = √65

    r'√65 = -8
    r' = 0.992 m/s

    Makes sense; since the boat is far away as compared to the height, the rope length is essentially the distance away, so dr/dt is about the same as dx/dt.

    The closer the boat gets, the slower the rope length decreases; when the boat is very near the dock, the rope length essentially stays at 1 meter.

  • Calculus -

    I like apples

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 an passing through the pulley on the deck that is 1m high than the bow of the boat ,if the rope is pulled im at the rate of 0.8m/s how fast does the boat approach …
  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

    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 …
  8. 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 …
  9. 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 …
  10. 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 …

More Similar Questions

Post a New Question