You are playing on the beach with your dog, Ohana. You throw the ball into the water at a point that is 14 m down the beach and 8 m from shore (see picture). Ohana can run on the sand at a rate of 6 m/s and swim at a rate of 1 m/s. What is the least time it can take Ohana, with some combination of running and swimming, to reach the ball? You and Ohana 14 m vq ball MA 8m B X
You are playing on the beach with your dog, Ohana. You throw the ball into the water at a point that is 14 m down the beach and 8 m from shore (see picture). Ohana can run on the sand at a rate of 6 m/s and swim at a rate of 1 m/s. What is the least time it can take Ohana, with some combination of running and swimming, to reach the ball? You and Ohana 14 m vq ball MA 8m B X
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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Transcribed Image Text:**Problem Statement:**
You are playing on the beach with your dog, Ohana. You throw the ball into the water at a point that is 14 meters down the beach and 8 meters from the shore (see picture). Ohana can run on the sand at a rate of 6 meters per second and swim at a rate of 1 meter per second. What is the least time it can take Ohana, with some combination of running and swimming, to reach the ball?
**Diagram Explanation:**
The diagram shows the scenario described in the problem.
- On the left, there is a point labeled "You and Ohana" on the beach.
- The beach is represented by a sandy area with a solid line indicating the border between water and land.
- A line segment measuring 14 meters represents the distance down the beach, parallel to the waterline, leading to where the ball lands in the water.
- Another line segment is perpendicular to this, measuring 8 meters from the shore to the ball’s position in the water.
- A solid dot marks Ohana’s starting position and the ball's landing position.
- The line from "You and Ohana" to the point in the water is divided into two parts: Ohana's run on the beach and swim in the water. The variable "x" marks the point along the 14-meter run from which Ohana will enter the water.
Consider optimizing Ohana's path by minimizing the time taken between running and swimming.
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