The method and the results are on the projectile motion lab. Do the analysis yourself first, then check the answers below.
Quick answer: Projectile motion is two-dimensional motion under gravity alone. These answers go with the AP Physics 1 lab on projectile motion: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
The model answers use the sample table. Your own measurements will differ a little, but the shapes of the graph and the method of analysis should be the same.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 1
2H ÷ g = 2 × 0.90 ÷ 9.81 = 0.1835 s², so t = 0.43 s.
Question 2 Launch speed
v = x ÷ t = 0.69 ÷ 0.428 = 1.6 m/s.
Question 3 Why x²
x = vt and t² = 2H ÷ g, so x² = v²t² = v² × 2H ÷ g. For a rolling ball v² is proportional to h, and 2H ÷ g is constant, so x² is proportional to h: the graph is a straight line through the origin.
x² = (v² ÷ h) × (2H ÷ g) × h, so v² ÷ h = gradient ÷ 0.1835 = 2.33 ÷ 0.1835 = 12.7 m/s². This is 91 % of 14.0 m/s²; the shortfall comes from friction at the ramp joint and air resistance, which remove kinetic energy.
Question 6 Uncertainty
Half the spread = (0.71 − 0.67) ÷ 2 = 0.02 m. Percentage uncertainty = 0.02 ÷ 0.69 × 100 = about 3 %.
Question 7 Improvement
Use a smoother join between ramp and table so the ball does not bounce; use a photogate or video to measure the speed directly; add more release heights and more trials. Also measure H more precisely with a longer rule. Best single change: photogate timing at the table edge.
