A boat on the ocean is 5 mi from the nearest point on a straight shoreline; that point is 15 mi from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. Complete parts (a) and (b) below. 5 mi 15mi- ... a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to minimize the total travel time? Let x be the distance between the nearest point on shore and the point she lands on shore. If T is the time it takes her to get to the restaurant, what is the objective function? T=D (Type an expression.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation.) To minimize the total travel time, the boat should land miles from the restaurant. (Type an exact answer, using radicals as needed.) b. If she walks at 3 mi/hr, find the minimum speed at which she must row so that the quickest way to the restaurant is to row directly (with no walking)? The minimum speed she must row is mi/hr. (Type an exact answer, using radicals as needed.)
A boat on the ocean is 5 mi from the nearest point on a straight shoreline; that point is 15 mi from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. Complete parts (a) and (b) below. 5 mi 15mi- ... a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to minimize the total travel time? Let x be the distance between the nearest point on shore and the point she lands on shore. If T is the time it takes her to get to the restaurant, what is the objective function? T=D (Type an expression.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation.) To minimize the total travel time, the boat should land miles from the restaurant. (Type an exact answer, using radicals as needed.) b. If she walks at 3 mi/hr, find the minimum speed at which she must row so that the quickest way to the restaurant is to row directly (with no walking)? The minimum speed she must row is mi/hr. (Type an exact answer, using radicals as needed.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A boat on the ocean is 5 mi from the nearest point on a straight shoreline; that point is 15 mi from a restaurant on the shore.
A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. Complete
parts (a) and (b) below.
5 mi
15 mi
a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to minimize the total travel time?
Let x be the distance between the nearest point on shore and the point she lands on shore. If T is the time it takes her to get to the restaurant, what is the objective
function?
T=
(Type an expression.)
The interval of interest of the objective function is
(Simplify your answer. Type your answer in interval notation.)
To minimize the total travel time, the boat should land
miles from the restaurant.
(Type an exact answer, using radicals as needed.)
b. If she walks at 3 mi/hr, find the minimum speed at which she must row so that the quickest way to the restaurant is to row directly (with no walking)?
The minimum speed she must row is mi/hr.
(Type an exact answer, using radicals as needed.)
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