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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.
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
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
and a drag force which always acts in the direction opposite to motion and is such that
where k is a non-negative 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 drag-free motion.
If there is no drag force (
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
We can first reproduce the velocity vector:
, 32 ,
, 32 6 Combining the vectors,
, , 32 In unit-vector notation,
Notice that the x and y components of the velocity vector remain constant. That is because there are
no forces in these directions. The z-component, on the other hand, changes according to
Now we reproduce the position vector:
, , 0,0, 32 0,0, 16 Combining the vectors,
Thus, the parametric equation of the trajectory are 16
Often problems are posed in two dimensions in the usual x-y plane with the force of gravity acting
vertically down along the y-axis. The equations that will ensue in that set up are:
In the more general cases where drag is not present, it is useful to write the position vector in
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 drag-free 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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This note was uploaded on 10/24/2012 for the course MAC 2313 taught by Professor Lopez during the Spring '10 term at Miami Dade College, Miami.
- Spring '10