Projectile motion explorer
A ball is thrown at 60° with the vertical. What is its angle with the horizontal, and how far does it go? Try it below, then change the numbers and see which answers stay the same.
Launch it yourself
Dashed: the 60° launch (from the horizontal), which lands at the same spot.
60° with the vertical is 30° with the horizontal. The formulas below always use the angle from the horizontal.
- Range R = u² sin 2θ / g
- 35.3 m
- Maximum height H = u² sin²θ / 2g
- 5.1 m
- Time of flight T = 2u sin θ / g
- 2.04 s
What to remember
- Read the angle first. “With the vertical” means subtract it from 90° before using the formulas: 60° with the vertical is 30° with the horizontal.
- The range is the same for two angles that add up to 90° (30° and 60°). It is largest at 45°.
- Maximum height uses sin²θ and divides by 2g; range uses sin 2θ and divides by g. They are different formulas, so check which one the question asks for.
- These results assume launch and landing at the same level, no air resistance and a constant g, as in the textbook derivation. Questions give g as 9.8 or 10 m/s², so use the one the question states.
Source: NCERT Class 11 Physics, Chapter 3 (Motion in a Plane), pages 39 and 40, as cited in our projectile motion lesson. Every number on this page is calculated from the three formulas above.
Ready for questions? Practise projectile motion questions with every wrong option explained.