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 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= m a = m/s (c) Obtain the expression for the acceleration vector a as a function of time (in m/s²). 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 = 16.7t and y = 3.64t - 4.90t2, where x and y are in meters and t 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= m a = m/s (c) Obtain the expression for the acceleration vector a as a function of time (in m/s²). 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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Scalars and Vectors

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Question

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

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