Work out projectile range instantly with clear inputs, formula shown and shareable results.
For launch and landing at the same height, the range is v^2 sin(2theta)/g. The sine of twice the angle peaks at 45 degrees, which is why that angle throws furthest, and why 30 and 60 degrees give identical ranges. At 20 m/s and 45 degrees the range is about 40.8 m with a 2.9 s flight.
Range
R = v^2 x sin(2theta) / g
Time of flight
t = 2v sin(theta) / g
Because sin(60) and sin(120) are equal. The steeper launch stays up longer but moves horizontally more slowly, and the two effects cancel exactly.
Yes. With drag the optimum drops to roughly 35-40 degrees, and lower still for light objects such as a shuttlecock.