Explanation Given information: The boat is located 4 ft above the bow of the boat. The distance of boat from the dock is y = 25 ft The rate at which the rope is being pulled is ft/sec . Calculation: let x be the distance between dock and boat. Here, the rope is being pulled in at the rate of 3 ft/sec . That is, the derivative d x d t = 3 ft/sec . Let the length of the rope at the time when the boat is at a distance of y ft from the dock be x . The diagram of the dock and boat is shown below in Figure 1, Figure (1) From Figure 1, the triangle is a right angle, Now, apply the Pythagorean Theorem to the right angle triangle in the above figure, x 2 = y 2 + 4 2 (1) Substitute 25 for y in the equation (1) to find the value of x . x 2 = ( 25 ) 2 + ( 4 ) 2 x 2 = 641 x = 641 = 25

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ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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Question

Chapter 3.6, Problem 58E

To determine

To find: The rate at which the boat approaches the dock.

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Chapter 3.6, Problem 57E

Chapter 3.6, Problem 59E

Chapter 3 Solutions

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The rate at which the boat approaches the dock.

Solution Summary: The author calculates the rate at which the boat approaches the dock. The distance of the rope is ft/sec.

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To find: The rate at which the boat approaches the dock.

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Chapter 3 Solutions