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Projectile Motion
We will start considering the motion of a projectile in 2 dimensions. The coordinate system that
will be used to describe the motion of the projectile consist of an x-axis (horizontal direction)
and a y-axis (vertical direction). Assuming that we are dealing with constant acceleration, we can
obtain the velocity and position of the projectile using the procedure outlined in Chapter 2:
where x
0
and y
0
are the x and y position of the object at t = 0 s, and v
x0
and v
y0
are the x and y
components of the velocity of the object at time t = 0.
Note that a
x
only affects v
x
and not v
y
,
and a
y
only affects v
y
.
In describing the motion of the projectile, we will assume that there is no acceleration in the x-
direction, while the acceleration in the y-direction is equal to the free-fall acceleration:
a
x
= 0
a
y
= - g = - 9.8 m/s
2
In this case, the equations of motion for the projectile are:
The trajectory of the projectile is completely determined by the equations of motion x(t) and y(t).
The coordinate system in which we will analyze the trajectory of the projectile is chosen such
that x
0
= y
0
= 0. In this case:
The time t can be eliminated from these two equations:
Substituting this expression for t into the equation of motion for y, the following relation between
x and y can be obtained:
We can conclude that the trajectory of the projectile is described by a parabola.
Note:
Often, the total velocity v
0
of the object at time t = 0 s and the angle [theta] between the
direction of the projectile and the positive x-axis is provided. From this information the
components of the velocity at time t = 0 s can be calculated:

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*Sign up* Figure 4.2. Projectile Motion.

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