Release values

Illustrative defaults only. Loading replaces all three values.
Speed at release; 0 or greater.
0–90° above horizontal; decimals accepted.
Release height above the flat landing surface; 0 or greater.

Selected distance

18.99 m

13 m/s at 37° from 2.1 m

Gravity-only comparison, measured horizontally from release to a flat landing surface.

Flight time
1.83 s
Peak above landing
5.22 m

Maximum at this speed

Ideal angle
41.9°
Ideal range
19.21 m
Range difference
0.22 m

Same speed and release height; only the angle changes. A 0.00 m difference means equal to the displayed precision.

Hold conditions fixed

The comparison holds release speed and height constant while changing only the angle. A person may release at a different speed when changing angle; that relationship is not modeled here. Event presets change starting values, not the physics.

The existing model uses g = 9.81 m/s². With vertical speed vᵧ = v sin θ, flight time is (vᵧ + √(vᵧ² + 2gh)) ÷ g; horizontal range is v cos θ × flight time. Peak height is h + vᵧ² ÷ (2g). For positive speed, the ideal angle is atan(v ÷ √(v² + 2gh)); it is 45° at zero release height.

The OpenStax projectile-motion equations describe this gravity-only setting. Air resistance, wind, aerodynamic lift, spin, implement shape and landing slope are absent. This is a comparison of ideal release setups, not an athlete prediction or technique prescription.

Results round to 0.01 m or s; angle display rounds to 0.1°. Trying the ideal angle uses its unrounded canonical value. Range starts at the release point, so it is not a rule-based official meet measurement from a circle or arc.