Problem

A woman at a point $ A $ on the shore of a circul…

02:42

Question

Answered step-by-step

Problem 49 Hard Difficulty

Solve the problem in Example 4 if the river is $ 5km $ wide and point $ B $ is only $ 5 km $ downstream from $ A $.

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Chris Trentman

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Watch More Solved Questions in Chapter 4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Video Transcript

whereas to solve the problem. An example. Four of this section if the river is five kilometers wide and the point B is only five kilometers downstream from the point A. So again drawing a diagram like an example. Four. We have a triangle with three points a B and C. Great. It's a right triangle and then we have another point. D on the side opposite of a and now we have the distance from A to C is five kilometers and the distance from a to B is five kilometers. I'm sorry. Sorry. B is only five kilometers downstream from a. This means the distance from B to C is five kilometers. Not for me to be now let's call this mystery distance, but from D to see X mm. Why so X is the distance downstream from the point directly across the river? Clearly now the running distance. This is the length of DB, which is five minus X and the rowing distance once they're on the river. This is the distance from a T. D. Using Pythagorean theorem. This is the square root of 25 plus X squared. Also, our rowing speed is six kilometers per hour and running speed is eight kilometers per hour. So it follows the total time running and rowing, which will call T F X. Well, this is our rowing distance divided by our rowing rates. Six. So we have the square root of X squared plus 25/6, plus the rowing running distance five minus X over the running speed eight. And it's clear from our picture that the domain includes all X between zero and five. Now we're trying to minimize this time so we'll take the derivative of t Want to solve t prime of X equals zero. So we get t prime of X equals. This is one half times X squared plus 25 the negative one half time is two x over six minus 1/8 mhm which is equal to yes x over or X, basically over six times the square root of X squared plus 25 minus 1/8. Again, we want to set this equal zero So this is X over six times the square root of X squared plus 25 equals 1/8. So we have eight x equals six times the square root of X squared plus 25 solving this radical equation, you can square both sides Eventually you should get seven. X squared equals 225 and so X is equal to the square root of 225 over seven, which is approximately 567 and recalled. The units are in kilometers now. The critical number that we have this is outside of our domain from 0 to 5 time the absolute minimum max in a closed interval. It therefore follows that our answer must be at the end points. So let's find t of zero and t of five t of zero. If you plug this in is approximately 1.46 and the unit is in ours and t of five. This is approximately 1.18 and again the unit isn't ours. Looking at these two times, we see the time is shorter when X equals five and so police T has an absolute men at X equals five. Therefore, what's the man's strategy? To minimize the time the man should row directly from point A to point B

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem

A woman at a point $ A $ on the shore of a circul…

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 2 / BC Educators

Catherine Ross

Anna Marie Vagnozzi

Caleb Elmore

Kristen Karbon

Calculus 2 / BC Courses

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

James Stewart

Calculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Caleb Elmore

Kristen Karbon

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Caleb Elmore

Kristen Karbon

James StewartCalculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Caleb Elmore

Kristen Karbon

James Stewart

Calculus: Early Transcendentals