   Chapter 2.8, Problem 22E

Chapter
Section
Textbook Problem

# 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 8 m from the dock? To determine

To find:

How fast the boat is approaching the dock when it is 8 m from the dock.

Explanation

1. Concept:

We can plot the figure from the given situation, and it looks like a right angle triangle.

Let x be distance of the boat from the dock.

2. Formula:

i. Pythagorean Theorem:

Hypoteneous2=Sum of squares of perpendicular sides

ii. Power rule of differentiation:

ddxxn=n*xn-1

iii. Chain rule of differentiation:

ddtfx=ddxfx*dxdt

3. Given:

dydt= 1m/s, x = 8

4

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