Projectile Motion
In this experiment we will study motion in two-dimensions.
An object which has
motion in both the X and Y direction has a two dimensional motion. We will first
determine at what velocity the ball is being fired from the firing mechanism, and then
with this knowledge and some calculations.
Determine how far the ball will travel
when it is fired at an angle other than the horizontal.
Theory:
In introductory physics courses, a projectile is an object which is given some
initial velocity, v
0
, and thereafter, subjected only to gravity.
This definition of a
projectile assumes that no force due to air resistance is acting on the projectile.
This assumption is approximately valid if the velocity of the projectile is
relatively small (less than 10 meters/sec) and the cross-sectional area of the object
is small, which will be the case in this experiment.
Since gravity is the only force
assumed to act on the object
after it is given its initial velocity
, the object will be
in free-fall in the vertical direction, and will move with a constant velocity in the
horizontal direction.
Consider an object projected horizontally with a velocity, v
ox
, from some initial
height, H, above the floor, as sketched below.
The object will travel a horizontal
distance, R, during the time it falls a vertical distance, H.
Since the velocity in the
horizontal direction is constant,
R = v
0X
t
[1]
Where t is the time that the object is in flight
(which is also the time it takes the object to
fall a distance H).
In
free
fall,
the
vertical
distance
moved
during a time interval, t, is given by the
equation,
y - y
o
= v
oy
t - (1/2)gt
2
[2]
where y
o
is the initial position of the object, g is the acceleration due to gravity
(about 9.8 m/sec
2
), and v
oy
is the initial velocity of the object in the vertical (y)
direction.
In equation [2], “up” is taken as the positive direction, and “down” is
H
R
v
ox