1. The motion of the particle is described by the system of the equations (two degrees of freedom, x(t)- horizontal, y(t)- vertical): x(t) = 4t-8, [m] y(t) = -3t²6t+ 45, [m] (a) Derive the components of the velocity (v, and vy) and the accelera- tion (az and ay). (b) Determine the initial position, the initial velocity, the acceleration, and the magnitudes of the initial velocity of the particle. (c) Determine the position, the velocity, and the magnitude of the ve- locity of the particle at t = 2 s (d) Calculoto the h ...
1. The motion of the particle is described by the system of the equations (two degrees of freedom, x(t)- horizontal, y(t)- vertical): x(t) = 4t-8, [m] y(t) = -3t²6t+ 45, [m] (a) Derive the components of the velocity (v, and vy) and the accelera- tion (az and ay). (b) Determine the initial position, the initial velocity, the acceleration, and the magnitudes of the initial velocity of the particle. (c) Determine the position, the velocity, and the magnitude of the ve- locity of the particle at t = 2 s (d) Calculoto the h ...
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Homework 1-2 Kinematic Equations 2-D
1. The motion of the particle is described by the system of the equations
(two degrees of freedom, r(t)- horizontal, y(t)- vertical):
6
(a) Derive the components of the velocity (v and vy) and the accelera-
tion (az and ay).
Y
(b) Determine the initial position, the initial velocity, the acceleration,
and the magnitudes of the initial velocity of the particle.
H
[x(t) = 4t-8, [m]
y(t) = -3t²6t+ 45, [m]
(c) Determine the position, the velocity, and the magnitude of the ve-
locity of the particle at t = 2 s
(d) Calculate the horizontal position r(t) of the particle, when the par-
ticle falls on the ground, such that y(t) = 0.
F6
(e) Calculate the velocity (components and magnitude) of the particle,
when the particle falls on the ground (terminal velocity).
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Transcribed Image Text:loads/PHY%202201%20Homework%201-2%20(4).pdf
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Homework 1-2 Kinematic Equations 2-D
1. The motion of the particle is described by the system of the equations
(two degrees of freedom, r(t)- horizontal, y(t)- vertical):
6
(a) Derive the components of the velocity (v and vy) and the accelera-
tion (az and ay).
Y
(b) Determine the initial position, the initial velocity, the acceleration,
and the magnitudes of the initial velocity of the particle.
H
[x(t) = 4t-8, [m]
y(t) = -3t²6t+ 45, [m]
(c) Determine the position, the velocity, and the magnitude of the ve-
locity of the particle at t = 2 s
(d) Calculate the horizontal position r(t) of the particle, when the par-
ticle falls on the ground, such that y(t) = 0.
F6
(e) Calculate the velocity (components and magnitude) of the particle,
when the particle falls on the ground (terminal velocity).
887
&
U
J
F7
* 00
8
► 11
FB
(
9
.
K
A
Fall 2022
O
F9
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)
0
F10
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F11
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+ 11
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=
Expert Solution
Step 1
Solution:
1. (a). The velocity and acceleration can be obtained by the given position vectors as a function of time. The velocity is obtained by differentiating the x and y with respect to time.
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