Question

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 at a rate of 1 m/s, how fast is the boat approaching the dock when it is 4 m from the dock?

Answer #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 the dock when it is 9 m
from the dock? (Round your answer to two decimal places.)

A boat is pulled into a dock by means of a rope attached to a
pulley on the dock (see the accompanying figure). The rope is
attached to the bow of the boat at a point 12 ft below the pulley.
How fast must the rope be pulled if we want the boat to approach
the dock at a rate of 8 ft/min at the instant when 105 ft of rope
is out? Round your answer to two decimal places.

A dinghy is pulled toward a dock by a rope from the bow through
a ring on the dock 7 ft above the bow. The rope is hauled in at the
rate of 1 ft/sec. Complete parts (a) and (b).
a. How fast is the boat approaching the dock when 25 ft of rope
are out?
b. At what rate is the angle theta changing at this
instant?

Question 1:
Two cars start moving from the same point. one travels south
at 48 mi/h and the other travels west at 20 mi/h. At what rate is
the distance between the cars increasing two hours later?
Question 2:
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...

A rope attached to a boat is being pulled in at a rate of 11
fps. If the water is 16 ft below the level at which the rope is
being drawn in, how fast is the boat approaching the wharf when 35
ft of rope are yet to be pulled in?

A hanging weight, with a mass of m1 = 0.355
kg, is attached by a rope to a block with mass
m2 = 0.845 kg as shown in the figure below. The
rope goes over a pulley with a mass of M = 0.350 kg. The
pulley can be modeled as a hollow cylinder with an inner radius of
R1 = 0.0200 m, and an outer radius of
R2 = 0.0300 m; the mass of the spokes is
negligible. As...

Two objects are connected to a rope, and the rope is hung over a
pulley connected to the ceiling, as shown in the figure below.
Two objects, labeled m1 and
m2, are connected to a rope which is hung over
a pulley connected to the ceiling. The pulley is of mass M
and radius R. An object labeled m1
hangs suspended off the surface on the left side of the pulley. An
object m2 is on the right side of...

Two carts, A and B, are connected by a rope 39 ft long that
passes over a pulley P. The point Q is on the
floor h = 12 ft directly beneath P and between
the carts. Cart A is being pulled away from Q at a speed
of 4 ft/s. How fast is cart B moving toward Q at the
instant when cart A is 5 ft from Q? (Round your answer to
two decimal places.)

Jack and Jill are maneuvering a 3400 kg boat near a dock.
Initially the boat's position is < 2, 0, 3 > m and its speed
is 1.1 m/s. As the boat moves to position < 4, 0, 2 > m, Jack
exerts a force of < -420, 0, 210 > N, and Jill exerts a force
of < 160, 0, 320 > N. How much work does Jack do?How much
work does Jill do? How much work does Jill...

Jack and Jill are maneuvering a 3400 kg boat near a dock.
Initially the boat's position is < 2, 0, 3 > m and its speed
is 1.1 m/s. As the boat moves to position < 4, 0, 2 > m, Jack
exerts a force of < -420, 0, 210 > N, and Jill exerts a force
of < 160, 0, 320 > N. How much work does Jack do?How much
work does Jill do? How much work does Jill...

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