## Problem StatementA 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 ExpressionWrite 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 ExpressionBy 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 ExpressionObtain the expression for the acceleration vector \(\vec{a}\) as a function of time (in m/s\(^2\)).\[\vec{a} = \boxed{}\]### (d) Vector Expressions at \(t = 2.85\) sNext, 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\(^2\).)\[\vec{r} = \boxed{}\]\[\vec{v} = \boxed{}\]\[\vec{a} = \boxed{}\]

Answered: Image /qna-images/answer/b09bf336-8fbe-4d79-9124-39d2dfd75d4c.jpg

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 - 4.90t2, 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 ✓ m/s (d) 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/s2.) = m m/s m/s²

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 - 4.90t2, 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 ✓ m/s (d) 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/s2.) = m m/s m/s²

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

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/s²
A 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?
A 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/s2
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.
Problem 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.
A 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.
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?
The 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.
A 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/s2
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.
B 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 51
Vector 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?