Unformatted text preview: speed have dimension [L]/[T] so if we were measuring distance in feet and
time in seconds, the speed would be approximately 5.85 feet/second.
Projectile Motion
Of all motions in space, projectile motion is the one that everyone is familiar with because it
represents the motion that an object experiences when it moves under the influence of the Earth’s
gravitational force and possibly other resistive forces such as air drag. The simplest motion is the
following:
above the ground with an initial
An projectile of mass
is fired from some initial height
. The forces acting on the object are the Earth’s gravitational force
,
,
velocity 0
and a drag force which always acts in the direction opposite to motion and is such that
where k is a nonnegative constant. We treat the general case in an optional section at the end of
these notes and limit ourselves to the more restrictive case of dragfree motion.
If there is no drag force (
parallel to
and take 0 . Let us set up a coordinate system in which the force of gravity is
32 ft/sec2. 0 , , 32 We wish to describe the projectile’s motion.
If there is no drag force, then the only force is that of gravity. The acceleration vector is therefore
32
We can first reproduce the velocity vector:
,
, 32 ,
, 32 6 Combining the vectors,
, , 32 In unitvector notation,
32
Notice that the x and y components of the velocity vector remain constant. That is because there are
no forces in these directions. The zcomponent, on the other hand, changes according to
32 .
Now we reproduce the position vector:
, , 0,0, 32 0,0, 16 Combining the vectors,
16
Thus, the parametric equation of the trajectory are 16
Often problems are posed in two dimensions in the usual xy plane with the force of gravity acting
vertically down along the yaxis. The equations that will ensue in that set up are:
16
In the more general cases where drag is not present, it is useful to write the position vector in
general terms:
1
0
0
2
The constant is the acceleration an object experiences due to the force of gravity. Its value is
approximately 9.8 m/s2 in the Metric System and, as was stated earlier, 32 ft/s2 in the English
system. This one formula can be used to solve any dragfree situation.
Example 5 Suppose a projectile is fired from ground level with a speed of 400 ft/sec at an angle of
45° with the horizontal. Determine the position ve...
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 Spring '10
 LOPEZ
 Equations, Vectors, Force, Sin, Cos

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