Projectile Motion Range

Students determine the muzzle velocity of a spring launcher from a horizontal shot, then use kinematics to predict and test the range of a projectile launched at selected angles over level and uneven terrain. The activity connects measured distances and heights to time of flight and horizontal range using constant-acceleration equations.

Determine Muzzle Velocity (Horizontal Launch)

1. Clamp the PASCO mini launcher securely at table height with the barrel set to 0 degrees (horizontal). Wear safety glasses.
2. Place the ball in the barrel and use the pushrod to cock the piston to the long-range setting (three clicks).
3. Fire one trial to locate the impact point on the floor. Tape a strip of paper to the floor aligned with the shot path to mark impacts.
4. Measure the vertical drop height from the marked launch point on the barrel (bottom of ball at exit) to the floor.
5. Fire several shots, marking each impact on the paper. Measure the horizontal distance from the floor point directly below the launch point to each mark.
6. Compute the average horizontal distance. Using the drop height, compute time of flight with \(t=\sqrt{2h/g}\). Compute muzzle speed with \(v_0=\bar{x}/t\). Record results.

Predict and Test Range on a Level Surface (Nonzero Angle)

1. Reposition the launcher so the projectile lands on the tabletop at the same height as launch.
2. Set a launch angle between 20 and 60 degrees, not 45 degrees. Record the angle.
3. Use the muzzle speed from Part A and the chosen angle to predict range on level ground with \(R=\frac{v_0^2\sin(2\theta)}{g}\).
4. Measure the predicted range on the tabletop and tape paper at that location to record impacts.
5. Shoot several trials, marking impact points. Compute the average measured range and compare to the prediction.

Predict and Test Range With Uneven Terrain (Different Landing Height)

1. Move the launcher to the table edge so the projectile lands on the floor at a lower height. Choose and record a launch angle.
2. Measure and record the vertical drop from launch height to the floor.
3. Predict the horizontal range using \(t=\frac{v_0\sin\theta+\sqrt{(v_0\sin\theta)^2+2gh}}{g}\) for time of flight to a lower landing level, then \(x=v_0\cos\theta\cdot t\).
4. Tape paper along the expected impact line, run several trials, and compute the average measured range. Compare to the prediction.

Projectile Motion Lab angle vs range - Physics for the Mass(es):

📄 Physics Lab – Projectile Motion - Milligan Physics: https://milliganphysics.com/Physics/PrjLabML.htm

• Repeat Part B with the complementary angle to check that ranges match on level ground.
• Test short, medium, and long spring settings to examine how range scales with launch speed.
• Investigate the effect of small angle changes (for example, 30, 35, 40 degrees) on range and plot.
• Use carbon paper or a target grid to capture impact scatter and analyze precision.
• Estimate air resistance by comparing measured range to ideal predictions at higher angles and speeds.

• Safety glasses required for all participants and observers.
• Always assume the launcher is loaded; keep fingers and face away from the muzzle.
• Clamp the launcher firmly with a C clamp; verify the table and clamp are stable before firing.
• Do not overtighten the angle thumb screw to avoid damaging the barrel ridges; tighten just enough to hold the angle.
• Ensure the downrange area is clear; use paper targets only and never aim at people or fragile objects.
• Load and cock only with the ball seated in the piston using the pushrod; never dry fire.
• Retrieve projectiles only after confirming the launcher is safe and the operator is not preparing to fire.

• How close are the measured ranges to the predicted values for level shots? (Compute percent difference to quantify agreement.)
• How does a different landing height change time of flight and range? (A lower landing height increases time aloft and range; a higher landing height decreases them.)
• What are likely sources of random error and systematic error in this lab? (Random: trigger release variability, reading distances, paper placement. Systematic: misread angle, incorrect height reference, air drag, barrel friction.)
• If your measured ranges are consistently short, what model assumption is being violated? (Neglect of air resistance and spin typically shortens range relative to ideal predictions.)