The drag-free motion of a particle is defined by the following component equations in the X, Y Cartesian coordinate system: 1. 2 h = (Vo cos α) t and Ty = (Vo sin α) t -, 1 2 where Vo-200 m/s, α-60° and g-9.81 m/s. At t-40 s, find the components of the velocity and acceleration vectors in the X, Y Cartesian coordinates. Draw vector diagrams of the velocity and acceleration vectors in the Cartesian coordinates, including the unit vectors. 2. The velocity components of a particle are given as The initial conditions of position are r t0)y(t). Att 1s: (a) Find the components of the position and acceleration vectors in the Cartesian coordinates. (b) Determine the velocity and acceleration components in the Polar coordinates (c) Draw vector diagrams to demonstrate that the same velocity and acceleration vectors are obtained for both the Cartesian and Polar coordinate systems. Use the vector diagrams to show the vector components, unit vectors, and units.

Question
The drag-free motion of a particle is defined by the following component equations in the X, Y
Cartesian coordinate system:
1.
2
h
= (Vo cos α) t and Ty = (Vo sin α) t
-,
1
2
where Vo-200 m/s, α-60° and g-9.81 m/s. At t-40 s, find the components of the
velocity and acceleration vectors in the X, Y Cartesian coordinates. Draw vector diagrams of the
velocity and acceleration vectors in the Cartesian coordinates, including the unit vectors.
2.
The velocity components of a particle are given as
The initial conditions of position are r t0)y(t). Att 1s:
(a) Find the components of the position and acceleration vectors in the Cartesian coordinates.
(b) Determine the velocity and acceleration components in the Polar coordinates
(c) Draw vector diagrams to demonstrate that the same velocity and acceleration vectors are
obtained for both the Cartesian and Polar coordinate systems. Use the vector diagrams to
show the vector components, unit vectors, and units.
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Transcribed Image Text

The drag-free motion of a particle is defined by the following component equations in the X, Y Cartesian coordinate system: 1. 2 h = (Vo cos α) t and Ty = (Vo sin α) t -, 1 2 where Vo-200 m/s, α-60° and g-9.81 m/s. At t-40 s, find the components of the velocity and acceleration vectors in the X, Y Cartesian coordinates. Draw vector diagrams of the velocity and acceleration vectors in the Cartesian coordinates, including the unit vectors. 2. The velocity components of a particle are given as The initial conditions of position are r t0)y(t). Att 1s: (a) Find the components of the position and acceleration vectors in the Cartesian coordinates. (b) Determine the velocity and acceleration components in the Polar coordinates (c) Draw vector diagrams to demonstrate that the same velocity and acceleration vectors are obtained for both the Cartesian and Polar coordinate systems. Use the vector diagrams to show the vector components, unit vectors, and units.