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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 = 19.9t and y = 3.60t - 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 i and j. (Give the answer in terms of t.) 7-19.9 +3.61 4.9² m 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.) 19.91 +3.6-9.8 m/s = (c) Obtain the expression for the acceleration vector a as a function of time (in m/s²). a = -9.8 x Did you take the derivative with respect to time of each component of the velocity vector expression? What should the magnitude and direction of the acceleration be in this case? m/s² (d) Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the metal ball at t = 2.76 s. (Assume the position is in m, the velocity is in m/s and the acceleration i in m/s².) 7 = V = a = Need Help? Read It m m/s m/s²

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 = 19.9t and y = 3.60t - 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 i and j. (Give the answer in terms of t.) 7-19.9 +3.61 4.9² m 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.) 19.91 +3.6-9.8 m/s = (c) Obtain the expression for the acceleration vector a as a function of time (in m/s²). a = -9.8 x Did you take the derivative with respect to time of each component of the velocity vector expression? What should the magnitude and direction of the acceleration be in this case? m/s² (d) Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the metal ball at t = 2.76 s. (Assume the position is in m, the velocity is in m/s and the acceleration i in m/s².) 7 = V = a = Need Help? Read It m m/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)...
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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 = 19.9t and y = 3.60t - 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.) 19.9 +3.6t 4.9² m 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 = 19.9i+ 3.6 9.8tj m/s (c) Obtain the expression for the acceleration vector a as a function of time (in m/s²). a = -9.8 Did you take the derivative with respect to time of each component of the velocity vector expression? What should the magnitude and direction of the acceleration be in this case? m/s² (d) Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the metal ball at t = 2.76 s. (Assume the position is in m, the velocity is in m/s and the acceleration is in m/s².) r = V = a = Need Help? Read It m m/s m/s²
Transcribed Image Text: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 = 19.9t and y = 3.60t - 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.) 19.9 +3.6t 4.9² m 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 = 19.9i+ 3.6 9.8tj m/s (c) Obtain the expression for the acceleration vector a as a function of time (in m/s²). a = -9.8 Did you take the derivative with respect to time of each component of the velocity vector expression? What should the magnitude and direction of the acceleration be in this case? m/s² (d) Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the metal ball at t = 2.76 s. (Assume the position is in m, the velocity is in m/s and the acceleration is in m/s².) r = V = a = Need Help? Read It m m/s m/s²
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