Homework Help is Here – Start Your Trial Now!
Science
Physics
A fish swimming in a horizontal plane has velocity V₁ = (4.00 +1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is ₁ = (15.0î - 1.70 ĵ) m. After the fish swims with constant acceleration for 18.0 s, its velocity is = (24.0 î - 6.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? (b) What is the direction of its acceleration with respect to unit vector î? (c) If the fish maintains constant acceleration, where is it at t = 30.0 s? In what direction is it moving? Part 1 of 7 - Conceptualize The fish is speeding up and changing direction in a horizontal plane relative to a known position vector. We will write separate equations to describe the x and y components of its motion under constant acceleration. Part 2 of 7 - Categorize We will model the fish as an object under constant acceleration. We use the standard equations for two dimensional motion in the xy plane. We will use x and y subscripts for the components of position, velocity, and acceleration. We know the initial velocity of the fish and its velocity after a certain period of time. We want to calculate the final position of the fish and its direction of motion after it swims for an additional period of time. Part 3 of 7 - Analyze We are given that at t = 0 s, V₁ = (4.00 Îî + 1.00 ĵ) m/s and ₁ = (15.0 î– 1.70 ĵ) m. After the fish swims for t = 18.0 s, we know that V₁ = (24.0 î - 6.00₁) m/s. (a) Write the x and y components ax and a, for the constant acceleration vector a. 24.0 m/s 1.70 X = Your response differs from the correct answer by more than 10%. Double check your calculations. m/s 18.0 s ay = = Avx At Avy At = m/s² m/s 1.00 m/s 18.0 s m/s²

A fish swimming in a horizontal plane has velocity V₁ = (4.00 +1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is ₁ = (15.0î - 1.70 ĵ) m. After the fish swims with constant acceleration for 18.0 s, its velocity is = (24.0 î - 6.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? (b) What is the direction of its acceleration with respect to unit vector î? (c) If the fish maintains constant acceleration, where is it at t = 30.0 s? In what direction is it moving? Part 1 of 7 - Conceptualize The fish is speeding up and changing direction in a horizontal plane relative to a known position vector. We will write separate equations to describe the x and y components of its motion under constant acceleration. Part 2 of 7 - Categorize We will model the fish as an object under constant acceleration. We use the standard equations for two dimensional motion in the xy plane. We will use x and y subscripts for the components of position, velocity, and acceleration. We know the initial velocity of the fish and its velocity after a certain period of time. We want to calculate the final position of the fish and its direction of motion after it swims for an additional period of time. Part 3 of 7 - Analyze We are given that at t = 0 s, V₁ = (4.00 Îî + 1.00 ĵ) m/s and ₁ = (15.0 î– 1.70 ĵ) m. After the fish swims for t = 18.0 s, we know that V₁ = (24.0 î - 6.00₁) m/s. (a) Write the x and y components ax and a, for the constant acceleration vector a. 24.0 m/s 1.70 X = Your response differs from the correct answer by more than 10%. Double check your calculations. m/s 18.0 s ay = = Avx At Avy At = m/s² m/s 1.00 m/s 18.0 s m/s²

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
See similar textbooks
icon
Related questions
icon
Concept explainers
Topic Video
Question
100%
**Title: Analyzing the Motion of a Fish in a Horizontal Plane** **Introduction** A fish swimming in a horizontal plane has an initial velocity given by \(\vec{v_i} = (4.00 \, \hat{i} + 1.00 \, \hat{j}) \, \text{m/s}\) and starts at a position relative to a rock at \(\vec{r_i} = (15.0 \, \hat{i} - 1.70 \, \hat{j}) \, \text{m}\). After swimming with a constant acceleration for 18.0 seconds, its velocity becomes \(\vec{v} = (24.0 \, \hat{i} - 6.00 \, \hat{j}) \, \text{m/s}\). **Objectives** 1. Find the components of the fish's acceleration. 2. Determine the direction of its acceleration concerning the unit vector \(\hat{i}\). 3. Calculate the position and direction of the fish at \(t = 30.0 \, \text{s}\). **Part 1 of 7 - Conceptualize** The fish changes speed and direction while swimming in a horizontal plane, modeled by constant acceleration. **Part 2 of 7 - Categorize** The fish is modeled under constant acceleration in two-dimensional motion (\(xy\) plane). Separate equations for \(x\) and \(y\) components help us understand position, velocity, and acceleration. **Part 3 of 7 - Analyze** Given: - \(\vec{v_i} = (4.00 \, \hat{i} + 1.00 \, \hat{j}) \, \text{m/s}\) - \(\vec{r_i} = (15.0 \, \hat{i} - 1.70 \, \hat{j}) \, \text{m}\) - Time \(t = 18.0 \, \text{s}\) - Final velocity: \(\vec{v_f} = (24.0 \, \hat{i} - 6.00 \, \hat{j}) \, \text{m/s}\) **(a) Calculate \(a_x\) and \(a_y\):** - \(a_x = \frac{\Delta v_x}{\Delta t} = \frac{24
Transcribed Image Text:**Title: Analyzing the Motion of a Fish in a Horizontal Plane** **Introduction** A fish swimming in a horizontal plane has an initial velocity given by \(\vec{v_i} = (4.00 \, \hat{i} + 1.00 \, \hat{j}) \, \text{m/s}\) and starts at a position relative to a rock at \(\vec{r_i} = (15.0 \, \hat{i} - 1.70 \, \hat{j}) \, \text{m}\). After swimming with a constant acceleration for 18.0 seconds, its velocity becomes \(\vec{v} = (24.0 \, \hat{i} - 6.00 \, \hat{j}) \, \text{m/s}\). **Objectives** 1. Find the components of the fish's acceleration. 2. Determine the direction of its acceleration concerning the unit vector \(\hat{i}\). 3. Calculate the position and direction of the fish at \(t = 30.0 \, \text{s}\). **Part 1 of 7 - Conceptualize** The fish changes speed and direction while swimming in a horizontal plane, modeled by constant acceleration. **Part 2 of 7 - Categorize** The fish is modeled under constant acceleration in two-dimensional motion (\(xy\) plane). Separate equations for \(x\) and \(y\) components help us understand position, velocity, and acceleration. **Part 3 of 7 - Analyze** Given: - \(\vec{v_i} = (4.00 \, \hat{i} + 1.00 \, \hat{j}) \, \text{m/s}\) - \(\vec{r_i} = (15.0 \, \hat{i} - 1.70 \, \hat{j}) \, \text{m}\) - Time \(t = 18.0 \, \text{s}\) - Final velocity: \(\vec{v_f} = (24.0 \, \hat{i} - 6.00 \, \hat{j}) \, \text{m/s}\) **(a) Calculate \(a_x\) and \(a_y\):** - \(a_x = \frac{\Delta v_x}{\Delta t} = \frac{24
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Projectile motion
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS