Question

Give your answer accurate to 3 decimal places.

A man on a dock is pulling in a boat by means of a rope attached to the bow of the boat at a point that is 1 ft above water
level. The rope goes from the bow of the boat to a pulley located at the edge of the dock 7 ft above water level. If he pulls
in the rope at a rate of 2 ft/sec, how fast (in feet per second) is the boat approaching the dock when the point of
attachment is 14 ft from the dock?

Answer 1

Therefore, The Boat is Approaching the Dock at a Rate of 2ft/sec When the point of attachment is: 14ft from the dock.

• Explanation:

Make a plan:

Let X be the Distance between the Boat and the Dock

Y be the Length of the Rope

We will use the Pythagorean Theorem to relate X and Y

Then Differentiate with respect to Time to find the Rate at which the Boat is Approaching the Dock.

• Solve Problem:

1 - Write the Pythagorean Theorem equation:

X^2 + 1^2 = Y^2

2 - Differentiate Both Sides with respect to Time (t):

2x dx/dt = 2y dy/dt

3 - Given dy/dt = -2ft/sec, and y = 14ft

Solve for, dx/dt, When X = 14ft

2(14)dx/dt = 2(14)( -2 )

4 - Solve For:

dx/dt

dx/dt = -2ft/sec

Draw the conclusion:

Therefore, The Boat is Approaching the Dock at a Rate of 2ft/sec When the point of attachment is: 14ft from the dock.

I hope this helps you!