Cannonball Shot

Aim a little desk cannon, choose how fast it fires, and try to land a steel ball right on the target.

Target
Result
Ready to fire
Flight time
0.00 s
Highest point
0.44 m
Distance
0.34 m

The maths, live

Split the launch vx = v cos θ, vy = v sin θvx = 5.36 m/s, vy = 4.50 m/s
Time in the air t = (vy + √(vy² + 2g y₀)) ÷ gt = 1.01 s (leaves the barrel 0.44 m up)
Landing distance x = x₀ + vx × tx = 5.74 m (target at 6 m)
Speed needed v = √(g x² ÷ (2cos² θ (x tan θ + y₀)))v = 7.18 m/s at 40°

Keep the speed the same and try 30° and 60°. They land in almost the same place. Which angle sends the ball furthest?

How it works

Once the ball leaves the barrel, the only big force on it is gravity, pulling it down. Its sideways speed stays the same, while its upward speed shrinks, then turns into a downward speed. Together they make a curved path called a parabola. A heavy steel ball hardly notices the air at these speeds, so real launchers in school labs land very close to these numbers.

Split the launch speed into a sideways part (v cos θ) and an upward part (v sin θ). The upward part decides how long the ball stays in the air, and the sideways part decides how far it travels in that time. On flat ground, 45° gives the longest shot, and pairs of angles like 30° and 60° land in almost the same place.

Try this

  1. Fire at 45° and find the speed that hits the middle target.
  2. Find two different angles that both hit the same target. Which one stays in the air longer?
  3. Keep the speed the same and change the angle. Which angle goes furthest?