Purpose: To determine the horizontal distance that a projectile will travel.
Background: Consider an object that is launched at an angle, as shown below.
It is important to remember that the arrow in the diagram above represents the velocity vector for the soccer ball, not the ball's actual path! The direction of the arrow indicates the ball's initial direction, and the length of the vector (if drawn to scale) indicates its magnitude. Remember, the ball follows a parabolic path; it does not follow a straight line!
Your first step in with an object launched at an angle should be to resolve the object's velocity into its components, as shown in the diagram below. We can then analyze the motion in each dimension (horizontal and vertical).
Looking at the horizontal motion, there is no acceleration since there are no horizontal forces acting after the launch of the projectile (as long as we are ignoring air resistance). All horizontal motion can then be described using the equation
dvwhere is the horizontal distance traveled by the projectile and is the horizontal xx
component of the projectile’s velocity. If we know the initial velocity, only the time is
needed to calculate the horizontal distance traveled. This can be found by analyzing the vertical motion.
Looking at the vertical motion, the only force acting is gravity; the acceleration 2will then be -9.8 m/s (taking up to be the positive direction). If we know the vertical
ddisplacement of the motion and the initial velocity, we can then use the equation y
to find the time that the projectile was actually in the air.
Hypothesis: none required
Materials: projectile launcher, meter stick, target
Procedure: Each group will be assigned an angle to use for this experiment. Upon receiving your angle, you will be required to calculate the horizontal distance that your projectile will travel. You are not permitted to launch the ball at your angle until all calculations have been completed!
You will need to determine the launch velocity of your “launcher” when the ball
is loaded. The only permitted trials to determine the launch speed are straight up.
After you have determined the initial launch velocity of the launcher, you must use this velocity along with the angle that you were assigned to calculate the horizontal distance that will be traveled by your projectile. You are required to make any other measurements of the apparatus required to perform these calculations.
Once you have calculated the horizontal distance that will be traveled by the projectile (and everyone in your group agrees with your result) you can proceed to actually launching your projectile. To do this, draw a straight line a piece of paper. This line will be your target. Tape the paper to the floor so that the line is exactly the proper distance away from your launcher. Place a piece of carbon paper over the target (shiny side up). Launch your projectile. If projectile does not hit the target paper, go back and check your calculations. Perform 4 or 5 more trials.
Observations: Record all data that you have collected in trying to determine the launch velocity of your projectile, as well as any data that you have recorded in order to calculate the horizontal distance of the projectile.
There should be 5 hits recorded on your target paper. Since you know how far away your target was, you can measure the actual distance traveled for each of the 5 trials. Record and average the 5 trials; these can then be compared with the calculated horizontal distance.
Analysis: Show all calculations that were used to find the launch velocity and horizontal distance traveled by the projectile. Explain the methods used and the reasons for performing these calculations. Comment on your success, or lack of, in hitting the target.
What errors were present in this lab? Have they been controlled? If not, why not? In what ways could the success of this lab be improved upon?
Conclusion: Is the mathematical model of projectile motion supported by your results?