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You are at a circular lake whose radius is 1 kilometer. You are on the east side of the lake and need to get to the west side as soon as possible. You can paddle through the water at 1.5 m/sec. (a) Suppose you can run with your kayak at 2 m/sec. What route should you take in order to arrive at the west side of the lake (with your kayak) in the least amount of time? (b) Suppose that you can run with your kayak at r m/sec. What is the smallest value of r for which it is better to run all the way around the lake than to do any paddling?

You are at a circular lake whose radius is 1 kilometer. You are on the east side of the lake and need to get to the west side as soon as possible. You can paddle through the water at 1.5 m/sec. (a) Suppose you can run with your kayak at 2 m/sec. What route should you take in order to arrive at the west side of the lake (with your kayak) in the least amount of time? (b) Suppose that you can run with your kayak at r m/sec. What is the smallest value of r for which it is better to run all the way around the lake than to do any paddling?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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You are at a circular lake whose radius is 1 kilometer. You are on the east side of the lake and need to get to the west side as soon as possible. You can paddle through the water at 1.5 m/sec. (a) Suppose you can run with your kayak at 2 m/sec. What route should you take in order to arrive at the west side of the lake (with your kayak) in the least amount of time? (b) Suppose that you can run with your kayak at \( r \) m/sec. What is the smallest value of \( r \) for which it is better to run all the way around the lake than to do any paddling? **USE OPTIMIZATION**
Transcribed Image Text:You are at a circular lake whose radius is 1 kilometer. You are on the east side of the lake and need to get to the west side as soon as possible. You can paddle through the water at 1.5 m/sec. (a) Suppose you can run with your kayak at 2 m/sec. What route should you take in order to arrive at the west side of the lake (with your kayak) in the least amount of time? (b) Suppose that you can run with your kayak at \( r \) m/sec. What is the smallest value of \( r \) for which it is better to run all the way around the lake than to do any paddling? **USE OPTIMIZATION**
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