Horizontal range

Beginner

Horizontal distance covered by a projectile on level ground.

Key relationR = u² sin2θ/g

On level ground R = u² sin2θ/g = ux·T. It depends on speed squared and the sine of twice the angle.

Worked example

u = 30 m/s at 45°: R = 900/9.8 ≈ 92 m.

Common mistake

The formula assumes launch and landing at the same level.

In more detail

The horizontal range of a projectile landing at its launch level is R = u² sin 2θ / g. It depends on both launch speed and angle.

Estimating how far a ball will travel when kicked.
Calculating the range of a water hose at a given angle.
Golfers and artillery planners use the range formula to estimate how far a ball or shell lands on flat ground.

How do I find the range?

Multiply the horizontal velocity by the time of flight, using the component of velocity in the x direction.

Does mass change the range?

Not when air resistance is ignored.

What is the range at a 30 degree angle compared with 45 degrees?

sin 60 degrees is about 0.87 while sin 90 degrees is 1, so 45 degrees gives the greater range.