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https//www.mathod com/Student/playerHomework aspo?homeworkdda4080546m8questionld 48eflushedsfalse&cld; 4302169&centenwina; JFC: Wilkerson-MAT 170-55Z1 Spring 2017 Justin Powell 44/17 843 AM Homework: Section 6.5 Score: 0 of 1 pt 9 of 9 (1 complete) HW Score: 25%, 3 of 12 pts Phys Sci 6.5.31 Assigned Media E Question Help Apulley is on the edge of a dock 9 feet above the water level Arope is being used topullinaboat Theropeis attached to the boat at water level The rope is being pulled inat the rate of 3 feet persecond Find the rate at which the boat is approaching the dock at the instant the boat is 2 feet from the dock The boat is approaching the dock at a rate of feet per second when the boat is 2 feet from the dock. (Round to the nearest thousandth as needed.) k Check Answ Enter your answer in the answer box and then C

Explanation / Answer

Height, h = 9 ft.
Distance from Dock, d = 2 ft.
Rope Length = L

Find dd/dt:

L² = d² + h²
L² = (2)² + (9)²
L² = 4 + 81
L² = 85
L = 85
L = 9.2

d² = L² - h²
d² = L² - 81

Differentiating Implicitly Over Time,

2d(dd/dt) = 2L(dL/dt) - 0
d(dd/dt) = L(dL/dt)
2(dd/dt) = 9.2(3)
2(dd/dt) = 27.6
dd/dt = 27.6 / 2
dd/dt = 13.8

The boat is approaching the dock at a rate of 13.8 ft./sec.

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