Lab 4 - Report Projectile Motion

Irvine Valley College Physics 4A Lab Report LAB 4: PROJECTILE MOTION Experiment Date: 5/7/22 Name: Email: Researcher : Analyst: PI:

LAB 5: PRELIMANARY CALCULATIONS Show the following calculations (including intermediate steps). Include appropriate units for the final results. 1. Four measurements of Range for a projectile launched horizontally are given by: R 1 = 120.8 cm ; R = 121.1 cm; R 3 = 121.5 cm R 4 = 121.7 cm a. Determine the mean range: R = 1 N ∑ i = 1 N R i = ¿ b. Determine the uncertainty of the mean range δ R = σ R = σ √ N = 1 √ N √ ∑ i = 1 N ( R − R i ) 2 N − 1 = ¿ 2. In the previous problem, the height of the launch is 82.0 cm. Determine the mean initial velocity of the launched projectile in units of m / s . v 0 = R √ g 2 h = ¿ 3. A graph of Range (in cm) vs. launch angle ϕ has a quadratic trendline fit equation of R =− .0371 ϕ 2 + 2.0118 ϕ − 119.5 . From this fit equation, determine the optimum launch angle ϕ opt . dR d ϕ | ϕ = ϕ opt = d d ϕ ( A ϕ 2 + B ϕ + C ) | ϕ = ϕ opt = 0 2 A ϕ opt + B = 0 ϕ opt = − B 2 A = ¿ Lab 5: Projectile Motion 2 of 8

LAB 5: PROJECTILE MOTION DATA Table 1. 0  measurements Height h±δh (cm) ± Angle ϕ ±δϕ (  ) ± Trial Range R±δR (cm) 1 ± 2 ± 3 ± 4 ± Lab 5: Projectile Motion 4 of 8

Table 2. Range measurements Angle ϕ ±δϕ (  ) Range R±δR (cm) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± GRAPH Attach a properly-formatted Excel graph of the data as detailed in the procedures. SAMPLE CALCULATIONS Lab 5: Projectile Motion 5 of 8

RESULTS Table 4. 0  calculations Mean Range R (cm) Uncertainty σ R (cm) Table 5. Excel-generated range equation R = A ϕ 2 + Bϕ + C A B C Table 6. Summary of results Mean Initial Speed v 0 ±δ v 0 (m/s) ± Optimal Angle ϕ opt (  ) Experimental Maximum Range R max ,experimental (cm) Theoretical Maximum Range R max ,theoretical (cm) Percent Error (%) Lab 5: Projectile Motion 7 of 8

QUESTIONS 1. The exact relationship between range and angle is via a trigonometric function. However, in the DATA ANALYSIS, you were instructed to insert a quadratic trendline for the Excel graph. Do the quadratic trendlines accurately fit the experimental data for the graph? Explain briefly. 2. Identify the independent variable(s) for this experiment. Be specific and use proper vocabulary. 3. Fixed variables are values which may or may not be known prior to making experimental measurements, or are measured during the experiment itself, but are held constant throughout the experiment. Identify the fixed variable(s) in this experiment. Be specific and use proper vocabulary. 4. Identify the dependent variable(s) for this experiment. Be specific and use proper vocabulary. CONCLUSION Lab 5: Projectile Motion 8 of 8