Chapter
3 Lab: Projectile Motion
BULL'S
EYE
PURPOSE
Predict where a steel ball will land when released from a certain height.
The final test of your measurements and computations will be to position an empty soup can so that the ball lands in the can the first time!
REQUIRED
EQUIPMENT/SUPPLIES
 ramp or
Hot Wheels track
 1/2inch
(or larger) steel ball
 empty
soup can
 meterstick
 plumb
line
 stopwatch,
tickertape timer; or computer light probes with interface light sources
DISCUSSION
Imagine
a universe without gravity. In this universe, if you tossed a rock where
there was no air, it would just keep goingforever. Because the rock
would be going at a constant speed, it would cover the same amount of
distance in each second. The equation for distance traveled when motion
is uniform is
x=vt
Then speed
is
v=x/t
Coming
back to earth, what happens when you drop a rock? It falls to the ground
and the distance it covers in each second increases. Gravity is constantly
increasing its speed. the equation of the vertical distance y
fallen after any time t is
y=1/2gt(squared)
where
g is the acceleration due to gravity. The speed v after time
t is
v=gt
What happens
when you toss the rock sideways? The curved motion that results can be
described s the combination of two straightline motions: one vertical
and the other horizontal. The vertical motion undergoes the acceleration
due to gravity, while the horizontal motion does not. The secret to
analyzing projectile motion is to keep two separate sets of books: one
that treats horizontal motion according to
x=vt
and the
other that treats the vertical motion according to
y=1/2gt(squared)
Horizontal
motion
 When thinking
about how far, think about x=vt.
 When thinking
about how fast, think about v=x/t.
Vertical
motion
 When thinking
about how far, think about y=(1/2)gt(squared).
 When thinking
about how fast, think about v=gt.
PROCEDURE
Step
One: Assemble your ramp. Make it as sturdy as possible so the steel
balls roll smoothly and reproducibly. the ramp should not sway or bend.
The ball must leave the table horizontally. Make the horizontal
part of the ramp at least 20cm long. The vertical height of the ramp
should be at least 30 cm.
Step
Two: Use a stopwatch or light probe to measure the time it takes
the ball to travel, from the first moment it reaches the level of the
tabletop to the time it leaves the tabletop. Divide this time interval
into the horizontal distance on the ramp to find the horizontal speed.
Release the ball from the same point (marked with tape) on the ramp from
each of the three runs.
1st time 
2nd time 
3rd time 
Average time 




Do not
permit the ball to strike the floor! Record the average horizontal speed
of the three runs.
horizontal
speed calculation:
Step
Three: Using a plumb line and a string, measure the vertical distance
h the ball must drop from the bottom end of the ramp in order
to land in an empty soup can on the floor.
1.
Should the height of the can be taken into account when measuring the
vertical distance h? if so, make your measurements accordingly.
h=____________
Step
4: Using the appropriate equation from the discussion, Calculate the
time it takes the ball to fall off the table and land
on the floor. Write the equation that relates h and t.
Which equation
for vertical distance? _____________
Show
your work in the following space.
t=______________
Step
5: The range is the horizontal distance of travel for a projectile off the table.
predict the range of the ball. write the equation you used and your
predicted range.
equation
for range:________________
predicted
rage R:__________________
Place
the can on the floor where you predict it will catch the ball.
ANALYSIS
2. Compare
the actual range of the ball with your predicted range. Compute the
percentage error.
3. What
may cause the ball to miss the target?
4. You
probably noticed that the range of the ball increased in direct proportion
to the speed at which it left the ramp. The speed depends on the release
point of the ball on the ramp. What role do you think air resistance
had in this experiment?
GOING
FURTHER
Suppose
you don't know the firing speed of the steel ball. If you go ahead and
fire it, and then measure its range rather than predicting it, you can
work backward and calculate the ball's initial speed. This is a good
way to calculate speeds in general! Do this for one or two fired balls
whose initial speeds you don't know.
