Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

A particle moves along the curve $ y = 2 \sin (\p…

01:25

Question

Answered step-by-step

Problem 23 Medium Difficulty

At noon, ship $ A $ is $ 100 km $ west of ship $ B. $ Ship $ A $ is sailing south at $ 35 km/h $ and ship $ B $ is sailing north at $ 25 km/h. $ How fast is the distance between the ships changing at $ 4:00 PM? $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Amrita Bhasin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Amrita Bhasin

Numerade Educator

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

More Answers

02:53

WZ

Wen Zheng

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 9

Related Rates

Related Topics

Derivatives

Differentiation

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Grace He
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Samuel Hannah

University of Nottingham

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

03:30

At noon, ship A is 100 km …

05:53

At noon, ship A is 150 km …

03:30

At noon, ship $A$ is 150 $…

01:31

At midnight ship $A$ is $5…

05:40

(Distance between ships) A…

06:05

At noon, ship $ A $ is $ 1…

09:28

Ships A and B leave port t…

04:55

Ships A and B leave port t…

Watch More Solved Questions in Chapter 3

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

Video Transcript

okay. Using the distance formula to figure out the distance between the two ships at time t we know we have 100 minus zero square. Plus, this is where variables come in 25 t post 35 t squared, which gives us DDT is the square root 10,000 plus 3600 t squared, which now tells us that deep prime of tea is gonna be one over two square root of 10 1000 plus 3600 t squared which simplifies to 1 80 t divided by the square root of 25 plus 90 squared, which tells us that deep REM of force notices just plugging in four is gonna be 1 80 times four divided by squirt of 25 plus nine times for squared, which is gonna be 55.38 kilometers per hour.

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.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
67
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
45
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Samuel Hannah

University of Nottingham

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

03:30

At noon, ship A is 100 km west of ship B. Ship A is sailing south at 35 km/h an…

05:53

At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and…

03:30

At noon, ship $A$ is 150 $\mathrm{km}$ west of ship B. Ship $\mathrm{A}$ is sai…

01:31

At midnight ship $A$ is $50 \mathrm{~km}$ north of ship $B$. Ship $A$ is sailin…

05:40

(Distance between ships) At 1: 00 p.m. ship $A$ is $25 \mathrm{km}$ due north o…

06:05

At noon, ship $ A $ is $ 150 km $ west of ship $ B. $ Ship $ A $ is sailing eas…

09:28

Ships A and B leave port together. For the next two hours, ship $\mathrm{A}$ tr…

04:55

Ships A and B leave port together. For the next two hours, ship A travels at 20…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started