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

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter1: Introduction And Vectors
Section: Chapter Questions
Problem 13OQ: Figure OQ1.13 shows two vectors D1 and D2. Which of the possibilities (a) through (d) is the vector...
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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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