College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Concept explainers
Question
![## Problem Statement
A polo ball is hit with a mallet off the edge of a cliff. Its \(x\)- and \(y\)-coordinates as functions of time are given by \(x = 16.8t\) and \(y = 3.72t - 4.90t^2\), where \(x\) and \(y\) are in meters and \(t\) is in seconds. (Do not include units in your answer.)
### (a) Position Vector Expression
Write a vector expression for the ball's position as a function of time (in m), using the unit vectors \(\hat{\imath}\) and \(\hat{\jmath}\). (Give the answer in terms of \(t\).)
\[
\vec{r} = \boxed{}
\]
### (b) Velocity Vector Expression
By taking derivatives, do the following:
Obtain the expression for the velocity vector \(\vec{v}\) as a function of time (in m/s). (Give the answers in terms of \(t\).)
\[
\vec{v} = \boxed{}
\]
### (c) Acceleration Vector Expression
Obtain the expression for the acceleration vector \(\vec{a}\) as a function of time (in m/s\(^2\)).
\[
\vec{a} = \boxed{}
\]
### (d) Vector Expressions at \(t = 2.85\) s
Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the polo ball at \(t = 2.85\) s. (Assume the position is in m, the velocity is in m/s and the acceleration is in m/s\(^2\).)
\[
\vec{r} = \boxed{}
\]
\[
\vec{v} = \boxed{}
\]
\[
\vec{a} = \boxed{}
\]](https://content.bartleby.com/qna-images/question/b4dca08d-d7c1-4511-81d7-e3b17171b463/b09bf336-8fbe-4d79-9124-39d2dfd75d4c/b92t8ee_processed.png)
Transcribed Image Text:## Problem Statement
A polo ball is hit with a mallet off the edge of a cliff. Its \(x\)- and \(y\)-coordinates as functions of time are given by \(x = 16.8t\) and \(y = 3.72t - 4.90t^2\), where \(x\) and \(y\) are in meters and \(t\) is in seconds. (Do not include units in your answer.)
### (a) Position Vector Expression
Write a vector expression for the ball's position as a function of time (in m), using the unit vectors \(\hat{\imath}\) and \(\hat{\jmath}\). (Give the answer in terms of \(t\).)
\[
\vec{r} = \boxed{}
\]
### (b) Velocity Vector Expression
By taking derivatives, do the following:
Obtain the expression for the velocity vector \(\vec{v}\) as a function of time (in m/s). (Give the answers in terms of \(t\).)
\[
\vec{v} = \boxed{}
\]
### (c) Acceleration Vector Expression
Obtain the expression for the acceleration vector \(\vec{a}\) as a function of time (in m/s\(^2\)).
\[
\vec{a} = \boxed{}
\]
### (d) Vector Expressions at \(t = 2.85\) s
Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the polo ball at \(t = 2.85\) s. (Assume the position is in m, the velocity is in m/s and the acceleration is in m/s\(^2\).)
\[
\vec{r} = \boxed{}
\]
\[
\vec{v} = \boxed{}
\]
\[
\vec{a} = \boxed{}
\]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 2 steps with 2 images
Knowledge Booster
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
- A small metal ball is kicked from the edge of a cliff. Its x- and y-coordinates as functions of time are given by x = 16.7t and y = 3.64t - 4.90t2, where x and y are in meters and t is in seconds. (Do not include units in your answer.) (a) Write a vector expression for the ball's position as a function of time (in m), using the unit vectors î and ĵ. (Give the answer in terms of t.) r= By taking derivatives, do the following. (b) Obtain the expression for the velocity vector v as a function of time (in m/s). (Give the answers in terms of t.) V= a = m (c) Obtain the expression for the acceleration vector a as a function of time (in m/s²). m/s² r = m/s (d) Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the metal ball at t = 3.24 s. (Assume the position is in m, the velocity is in m/s and the acceleration is in m/s².) a = m m/s m/s²arrow_forwardA vector has both a direction and a "magnitude", or length. An example of a vector quantity is the wind, which has both a direction and a strength. What is the magnitude of the vector 32+ -93 +7k?arrow_forwardA golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by x = 17.2t and y = 4.16t − 4.90t2, where x and y are in meters and t is in seconds. (a) Write a vector expression for the ball's position as a function of time, using the unit vectors î and ĵ. (Give the answer in terms of t.) = m By taking derivatives, do the following. (Give the answers in terms of t.) (b) obtain the expression for the velocity vector as a function of time = m/s(c) obtain the expression for the acceleration vector as a function of time = m/s2(d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 3.18 s. = m = m/s = m/s2arrow_forward
- Vector R has a magnitude of 10 m. Its z component is 8 m. What are the possible values for its y component? Express your answer in meters. If there is more than one answer, separate them by a comma.arrow_forwardProblem 8: Consider two vectors A and B, expressed in unit vector notation as A= aji+ azj and B = bji+ bzj. A. Part (a) Enter an expression for the vector sum A + B in terms of quantities shown in the expressions above. A+B = B 7 8 HOME a i j k 4 5 6 a1 a2 bị 1 2 3 b2 d + END - h VO BACKSPACE CLEAR m DEL Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback. Part (b) Enter an expression for the difference vector A - B in terms of quantities shown in the expressions above. Part (c) Enter an expression for the square of the magnitude of the sum vector |A + B| in terms of quantities shown in the expressions above.arrow_forwardA velocity vector has a magnitude of 1.85 m/s and makes an angle of 155 ̊ with the +x axis.(a) Sketch a diagram of the vector and show the x and y components.(b) Calculate the x and y components of the vector.arrow_forward
- The magnitude of Ais 5.5 m, and this vector lies in the second quadrant and makes an angle of 34 ° with the +y-axis. What is the x-component?arrow_forwardThe x-component of a velocity vector that has an angle of 35 ∘ to the +x axis has a magnitude of 4.9 m/s. What is the magnitude of the velocity? Express your answer using two significant figures. What is the magnitude of the yy-component of the velocity? Express your answer using two significant figures.arrow_forwardA golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by x = 17.0t and y = 4.20t − 4.90t2, where x and y are in meters and t is in seconds. (a) Write a vector expression for the ball's position as a function of time, using the unit vectors î and ĵ. (Give the answer in terms of t.) = m By taking derivatives, do the following. (Give the answers in terms of t.) (b) obtain the expression for the velocity vector as a function of time = m/s(c) obtain the expression for the acceleration vector as a function of time = m/s2(d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 3.24 s. = m = m/s = m/s2arrow_forward
- An object has an initial velocity of 29.0 m/s at 95.0° and an acceleration of 1.90 m/s2 at 200.0°. Assume that all angles are measured with respect to the positive x-axis. (a) Write the initial velocity vector and the acceleration vector in unit vector notation. (b) If the object maintains this acceleration for 12.0 seconds, determine the average velocity vector over the time interval. Express your answer in your unit vector notation.arrow_forwardB U Bx = 12.2 cm. Consider vector B pictured below and the given length for Bx = 12.2cm and 0 = 24.0 What is the length (the hypotenuse) of vector B ? 2 51arrow_forwardVector A has a magnitude of 15.0 units and it points in a direction 310° counterclockwise from the positive x-axis. What are the x- and y-components of A?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press 
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
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...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON