YSP Physics Teaching Team

Ballistics Demonstration

Objectives:

To demonstrate to students the laws of physics as they relate to ballistics and kinematics.

Materials:

Students divided into groups of 4; 1-3 water balloon launchers; 3 water balloons per group; Protractor; String; Small weight; Calculators; Spring Scale

Background

Physics can tell us a great deal about how a projectile will move through the air and the effect that gravity will have on it. The purpose of this experiment is put into practice many of the basic formulas you have learned in kinematics, and apply them to a real life ballistics problem, of the type that was used in artillery calculations before computers were available.

Part I: Elevation!

Your group has been enlisted by the YSP Water Balloon Artillery Team to test out a top secret water balloon launcher. For this, one of the brave, or foolish, YSP team leaders will stand at a position approximately 20 m directly in front of you. You must calculate the correct angle (Ó¨) at which to apply a force of 15 lbs and successfully hit our stationary human target. The following information might be helpful to review:

Vx = V cos Ó¨

Vy = V sin Ó¨

Sx = Sxo + Vxo * t + .5 * g * t2

F = m * a

(remember force is measured here by our scale)

a = (V2 – V1) / t

Part II: Maximizing Your Range

After successfully soaking the YSP traitor, you have orders to try and water balloon the faculty meeting, which is being held on the other side of the hill, just beyond where you can see. To accomplish this, you’ll need to launch the balloons as far as possible given your equipment. Experiment with different angles (and a constant force) to determine the angle which gives the balloon the furthest range of flight. Predict your maximal range given that angle and the same constant force. The following formula could be useful in soaking the teachers:

S = (vo2 / g) * sin (2Ó¨)

Note that the above is a special case of the range formula, valid only when the initial and final heights are the same. From studying the above equation, what angle would you predict to give the longest range? Do your measurements agree with your theory?

Part III: Hanging Tough

We’ve dried off our dastardly YSP volunteer, but he’s learned a bit from his first experience. He’s initially suspicious now whenever he sees anyone fire a projectile at him, thus making it more difficult to complete your mission. Lucky for you, his attention span is shorter than the bump on his head, and he forgets all about any impending danger after 3 seconds. Thus, your only chance to once again nail the target 20 m away will be to keep your balloon up in the air for as long as possible, while still maintaining your accuracy. Calculate the angle and force you would choose, making use of any of the equations above, or any you know from previous lessons.