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?

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 46SE: Near the surface of the moon, the distance that an object falls is a function of time. It is given...
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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?
Step 1
Using the diagram below, find the relation between x and y.
= x2 + 1
y?
pulley
1
rope
Step 2
We must find dx/dt. Differentiating both sides gives us the following.
dy
2y ·
dy
= 2x. ax
dt
dt
dt
Step 3
Substituting for dy/dt gives the following.
2y ·
2x
dt
Submit Skip (you cannot come back)
Transcribed Image Text: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? Step 1 Using the diagram below, find the relation between x and y. = x2 + 1 y? pulley 1 rope Step 2 We must find dx/dt. Differentiating both sides gives us the following. dy 2y · dy = 2x. ax dt dt dt Step 3 Substituting for dy/dt gives the following. 2y · 2x dt Submit Skip (you cannot come back)
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