The questions are on the projectile motion test. Take it under real conditions before reading the mark scheme.
Quick answer: Projectile motion is two-dimensional motion under gravity alone. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics 1 test on projectile motion, from acceleration at the top to equal ranges, with the equivalent answers to accept.
The answers give the expected method and the mark allocation. Award marks for correct reasoning even if an earlier arithmetic slip carries through to the final value.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 1
Question 1 Acceleration at the top (1 mark)
It is 9.81 m/s² downward, the same as everywhere else on the path.
Marking: 1 mark, needs both magnitude and direction.
Question 2 Horizontal velocity (1 mark)
No horizontal force acts (air resistance ignored), so ax = 0 and vx is constant.
Marking: 1 mark for no horizontal force or zero horizontal acceleration.
Question 3 Cliff throw (5 marks)
- 20 = ½ × 9.81 × t², so t = √(40 ÷ 9.81) = 2.02 s.
- x = 15 × 2.02 = 30 m.
- vy = 9.81 × 2.02 = 19.8 m/s; speed = √(15² + 19.8²) = 25 m/s.
Marking: (a) 1 for the equation, 1 for the answer; (b) 1; (c) 1 for vy, 1 for the speed.
Question 4 Components (2 marks)
- 24 cos 35° = 19.7 m/s.
- 24 sin 35° = 13.8 m/s.
Marking: 1 mark each, correct trigonometric function and value.
Question 5 Boat on a river (3 marks)
- t = 100 ÷ 4.0 = 25 s.
- Drift = 3.0 × 25 = 75 m.
- v = √(4.0² + 3.0²) = 5.0 m/s.
Marking: 1 mark for each part.
Question 6 Kicked ball (4 marks)
- vy0 = 22 sin 45° = 15.56 m/s; T = 2 × 15.56 ÷ 9.81 = 3.2 s.
- vx = 15.56 m/s; R = 15.56 × 3.172 = 49 m.
Marking: (a) 1 for vy0, 1 for T; (b) 1 for vx, 1 for R.
Question 7 Explain the landing (2 marks)
The vertical motion is identical for both balls: each starts with zero vertical velocity and accelerates downward at 9.81 m/s² over the same height. Horizontal velocity has no effect on the vertical motion, so the fall time is the same.
Marking: 1 for equal vertical conditions, 1 for independence of the two motions.
Question 8 Equal ranges (2 marks)
The ranges are equal. R = v² sin 2θ ÷ g, and sin 60° = sin 120°, so the 30° and 60° launches (complementary angles) give the same range.
Marking: 1 for equal, 1 for the reason.
