World 1 · Kinematics · 7 minProjectile Range
The classic 45° cannon shot
Teaching this? Open projector mode
Launch at an angle and the range depends on both speed and angle: R = v²·sin(2θ) / g. On level ground, 45° gives the maximum range.
Which launch angle sends a projectile the farthest on flat ground?
The cannon below launches from the floor, so the ball comes down to the level it started from: the level ground of the formula. Its range is read where the ball’s centre returns to the launch level. The engine steps every 1/60 s and its ball lands exactly one step early, so its range is one step of sideways travel (v·cosθ × 1/60 s) short of the formula.
At the same speed on level ground, a 30° launch and a 60° launch land…
On level ground at 45°, the launch speed is doubled from 7 m/s to 14 m/s. The range becomes about…