## 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\(^2\).)\[\vec{r} = \boxed{}\]\[\vec{v} = \boxed{}\]\[\vec{a} = \boxed{}\]

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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)...

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