A soccer ball is kicked in such a manner that the x and y components of its position at any time are given by x = (19.1 m/s)t and y = (14.7 m/s)t (4.90 m/s²)t², where x and y will be in meters when t is in seconds. (a) Determine expressions for the x and y components of its velocity at any time. (Use the following as necessary: t.) Vx= ay = (b) Determine expressions for the x and y components of its acceleration at any time. (Use the following as necessary: t.) ax= m/s² m/s v(t = 1.64 s) = m/s a(t = 1.64 s) = (c) Determine expressions for the position, velocity, and acceleration vectors of the ball at the time t = 1.64 s. (Express your answer in vector form.) r(t = 1.64 s) = 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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A soccer ball is kicked in such a manner that the x and y components of its position at any time are given by x = (19.1 m/s)t and y = (14.7 m/s)t – (4.90 m/s²)t², where x and y will be in meters when t is in seconds.
(a) Determine expressions for the x and y components of its velocity at any time. (Use the following as necessary: t.)
=
=
(b) Determine expressions for the x and y components of its acceleration at any time. (Use the following as necessary: t.)
ax
m/s²
v(t = 1.64 s)
m/s
=
m/s
(c) Determine expressions for the position, velocity, and acceleration vectors of the ball at the time t = 1.64 s. (Express your answer in vector form.)
r(t = 1.64 s):
=
a(t = 1.64 s) =
m/s²
m
m/s
m/s²
Transcribed Image Text:A soccer ball is kicked in such a manner that the x and y components of its position at any time are given by x = (19.1 m/s)t and y = (14.7 m/s)t – (4.90 m/s²)t², where x and y will be in meters when t is in seconds. (a) Determine expressions for the x and y components of its velocity at any time. (Use the following as necessary: t.) = = (b) Determine expressions for the x and y components of its acceleration at any time. (Use the following as necessary: t.) ax m/s² v(t = 1.64 s) m/s = m/s (c) Determine expressions for the position, velocity, and acceleration vectors of the ball at the time t = 1.64 s. (Express your answer in vector form.) r(t = 1.64 s): = a(t = 1.64 s) = m/s² m m/s m/s²
Expert Solution
Step 1

a)

Calculate the x-component of the velocity.

vx=dxdtvx=ddt(19.1 m/s)tvx=19.1 m/s

Calculate the y-component of the velocity.

vy=dydtvy=ddt[(14.7 m/s)t(4.90 m/s2)t2]vy=14.7 m/s(9.80 m/s2)t

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