Physics "Phun" for Shooters

Problem Notes:

Introduction:
What path does a projectile follow in reaching its target?

There are two possible paths: one a smash down from above and the other a more direct. The shape of the path is not straight but an arc. This can be demonstrated with water or a launcher. These demonstrations are good for identifying significant variables for futrther investigation. (initial velocity, launch angle )

Investigation:
What is the range of a projectile?


There are many launchers used in sport games. These include: dart, paint ball, pellet, and BB . . . guns; projectiles launched by the body like: javelins, discus, shot-put, and balls . . . not to mention the many video games so popular with shooters.

With both the knowledge of physics and skill you can be more accurate than the guessing competition.

Experimenting can find the maximum range of the launcher however, knowledge of the laws of physics and some "phun" is also useful. The physics "phun" may increase competitive edge for example, it may be of advantage to know the range the projectile will fly at a particular launch angle.

How easy is it to find the angle necessary to shoot a projectile a particular distance? First, please consider, there are two significant variables here, one is obviously the energy behind the launch. What is the other? All variables must be controlled except the launch angle if we are to find its effect on the range of the projectile.

"Phun" in the concrete:
Overview of activities to develop understanding of projectile behaviour:

  1. A qualitative launcher game, "Artillery"
  2. An elastic launcher, of simple design, of which you will predict and test the range characteristics of a low speed projectile.
  3. Bonus Part- A launcher of your choosing for which you will do a theoretical investigation and then test its significant characterestics.

1- Play the "Artillery" game with a friend.
Write a summary of your rules for adjusting the range of the cannon which gives you your competitive edge.
Please be sure to explain what affect the angle and the 'powder load' have on the ranging of the shot.
2-
Make a launcher with a metre stick, two mail bundle elastics and a large washer. (The washer must be large enough to make the elastic mass insignificant.)
DIAGRAM:






Experiment to find how the vertical height changes with the stretch of the elastic. Include the stretch required to just barely nick the ceiling. Graph the result. Bonus will be given for using a spreadsheet and chart function.

PROVIDE SOLUTIONS FOR THE FOLLOWING PROBLEM:
Use the elastic stretch which projects the washer to touch the ceiling and
Find at least one angle for shooting the washer projectile in a garbage can size chalk circle : 4m away. Summarize your observations in the table below indicate experimental reliability.
h (vert. height) angle d (range) Find, by experiment, the launch angle necessary for a given range and vertical height : the height when shot straight up.
Summarize your observations in the table below.
d (target-range) height ( max straight up) launch angle

Prove the theoretical accuracy
with experimental reliability of at least 3/5 baskets.
If you are using this activity on the computer, change the numbers in Bold only.
Spreadsheet theoretical angle calculator. Max./Min . angle is calculated with a 5% uncertainty in the vertical height.

Max./Min . range is calculated with a 5% uncertainty in the launch angle.


Predicting the Launch angle(given the range and maximum vertical Height)








4 Bonus Part- Construct and or test a launcher of your choosing for which you will predict and test. This is the ENERGISER level. A computer generated report with appropriate calculating spread sheets and test results with uncertainties are all expected at this level. You may have a partner.

Name: _________________________________ Date:

What is the Range of a Projectile?
(Developing Understanding)

  1. If the shooter with a vertical height of 3m is shot at an angle of between 60o- 45o how would you expect the maximum height during its' flight to compare with the vertical height when shot straight up?
    The maximum height during its' flight at an angle less than 90o would be less than the vertical height when shot straight up
  2. How does this knowledge help you solve for the range of a projectile?
    The maximum range would be where half of the projectile energy is in the horrizontal velocity and half of the energy keeps the projectile in the air
    3 Show how the range is affected by the max vertical height launched straight up.
    (Assume the launch angle is 50o)
    It is expected greater max vertical height launched straight up will give greater range.
    4 Show how the range is affected by the launch angle.
    (Assume the vertical height is 4m)

It is expected the launch angle will give maximum range at 45o and each side of 45o will decrease the range, while those above 45o give more reliable ranges.
51 What is the launch angle for maximum range?
The launch angle for maximum range =45o

6 Write an explination for a grade 6 student which will help make them more accurate shooters.
The explination should include a discussion of two variables:
- the energy: strength of the shot
- the angle of launch