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 = 17.8t and y = 4.28t - 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 j. (Give the answer in terms of t.) r = 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.) m/s (c) Obtain the expression for the acceleration vector a as a function of time (in m/s2). m/s?
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 = 17.8t and y = 4.28t - 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 j. (Give the answer in terms of t.) r = 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.) m/s (c) Obtain the expression for the acceleration vector a as a function of time (in m/s2). m/s?
College Physics
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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 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 \( x = 17.8t \) and \( y = 4.28t - 4.90t^2 \), 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 \( \hat{i} \) and \( \hat{j} \). (Give the answer in terms of \( t \).)
\[
\vec{r} = \boxed{}
\]
### By taking derivatives, do the following.
### (b)
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)
Obtain the expression for the acceleration vector \( \vec{a} \) as a function of time (in m/s\(^2\)).
\[
\vec{a} = \boxed{}
\]
### (d)
Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at \( t = 2.73 \, \text{s}. \) (Assume the position is in m, the velocity is in m/s and the acceleration is in m/s\(^2\).)
\[
\vec{r} = \boxed{}
\]
\[
\vec{v} = \boxed{}
\]
\[
\vec{a} = \boxed{}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc618d345-2f4b-4ba3-b2cb-33f4f1942e28%2F50195c56-645e-4eea-8319-8321c757553e%2F7k4g6xg_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 \( x = 17.8t \) and \( y = 4.28t - 4.90t^2 \), 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 \( \hat{i} \) and \( \hat{j} \). (Give the answer in terms of \( t \).)
\[
\vec{r} = \boxed{}
\]
### By taking derivatives, do the following.
### (b)
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)
Obtain the expression for the acceleration vector \( \vec{a} \) as a function of time (in m/s\(^2\)).
\[
\vec{a} = \boxed{}
\]
### (d)
Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at \( t = 2.73 \, \text{s}. \) (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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