Answer key: Projectile Motion Worksheet
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Goal: Investigate how launch angle, launch speed and gravity change a projectile’s range, peak height and flight time, and explain the results with the projectile formulas.
Completed results table
| Setting | Range | Peak height | Flight time |
|---|---|---|---|
| 20 m/s at 45° (Maximum range) | 40.775 m | 10.194 m | 2.883 s |
| 20 m/s at 30° | 35.312 m | 5.097 m | 2.039 s |
| 20 m/s at 60° | 35.312 m | 15.291 m | 3.531 s |
| 20 m/s at 25° (Low arc) | 31.235 m | 3.641 m | 1.723 s |
| 40 m/s at 45° | 163.099 m | 40.775 m | 5.766 s |
| 20 m/s at 45°, Moon gravity | 246.914 m | 61.728 m | 17.459 s |
Answers
Compare the 30° and 60° launches. What is the same and what is different? Use the range formula R = v₀² sin(2θ) / g to explain.
Both land 35.31 m away, because sin(2 × 30°) = sin(2 × 60°): complementary angles give the same range on level ground. The 60° launch climbs higher (15.29 m instead of 5.10 m) and stays up longer (3.53 s instead of 2.04 s), because more of its speed is vertical.
Which angle gave the longest range at 20 m/s? Why is 45° the best angle in this model?
45°, with a range of 40.77 m. Range is v₀² sin(2θ) / g, and sin(2θ) is largest (1) when 2θ = 90°. On real slopes or with air resistance the best angle changes.
Doubling the launch speed from 20 m/s to 40 m/s multiplied the range by what factor? Explain using the formula.
By 4, from 40.77 m to 163.10 m. Range depends on v₀², so twice the speed gives 2² = 4 times the range. The peak height also grows 4 times and the flight time doubles.
On the Moon (g = 1.62 m/s²), how much farther did the same launch go? Explain the factor.
About 6 times farther: 246.91 m instead of 40.77 m. Range is inversely proportional to g, and 9.81 ÷ 1.62 ≈ 6.06. The flight lasts 17.46 s.
At 20 m/s and 45°, the horizontal speed stays 14.14 m/s for the whole flight. Why doesn’t gravity change it?
Gravity pulls straight down, so it only changes the vertical velocity. With no air resistance there is no horizontal force, so the horizontal velocity v₀ cos θ = 20 × cos 45° = 14.14 m/s stays constant.
Challenge: which other launch angle gives the same range as 25° at 20 m/s? Predict, then check it in the lab.
65°. Complementary angles (adding to 90°) give the same range on level ground, so both 25° and 65° land 31.24 m away.