======Projectile Motion Range======


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**Difficulty: **{{$demo.difficulty_description}}\\
**Safety: **{{$demo.safety_description}}\\
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**Categories:** {{$demo.categories}}
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====Summary====                   
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====Procedure====  
Determine Muzzle Velocity (Horizontal Launch)  
  - Clamp the PASCO mini launcher securely at table height with the barrel set to 0 degrees (horizontal). Wear safety glasses.  
  - Place the ball in the barrel and use the pushrod to cock the piston to the long-range setting (three clicks).  
  - 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.  
  - Measure the vertical drop height from the marked launch point on the barrel (bottom of ball at exit) to the floor.  
  - 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.  
  - 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)  
  - Reposition the launcher so the projectile lands on the tabletop at the same height as launch.  
  - Set a launch angle between 20 and 60 degrees, not 45 degrees. Record the angle.  
  - Use the muzzle speed from Part A and the chosen angle to predict range on level ground with \(R=\frac{v_0^2\sin(2\theta)}{g}\).  
  - Measure the predicted range on the tabletop and tape paper at that location to record impacts.  
  - 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)  
  - Move the launcher to the table edge so the projectile lands on the floor at a lower height. Choose and record a launch angle.  
  - Measure and record the vertical drop from launch height to the floor.  
  - 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 \(x=v_0\cos\theta\cdot t\).  
  - Tape paper along the expected impact line, run several trials, and compute the average measured range. Compare to the prediction.




====Links==== 
Projectile Motion Lab angle vs range - Physics for the Mass(es): 
{{youtube>w0NFRiCW24E?}}\\

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


====Variations====
  * 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 Precautions====
  * 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.




====Questions to Consider====
  * 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.)