Free interactive tool

Projectile Motion Simulator

Speed and angle in, arc out — with range, peak height, and flight time live.

Motion lab

Launch and land on arithmetic

Set speed and angle; the arc, range, and flight time obey the constant-gravity equations.

Every projectile question hides the same two ideas: horizontal speed never changes, and gravity owns the vertical. The 45° maximum range is where the two split the budget evenly.

  • Confirm that 30° and 60° land in the same place.
  • Double the speed and watch what happens to the range — twice, or more?

Every projectile problem hides the same two ideas: horizontal speed never changes, and gravity owns the vertical. The arc, range, and hang time all follow from launch speed and angle.

Confirm the classics interactively: 45° maximizes range on flat ground, and 30° lands exactly where 60° does.

Why is 45 degrees optimal?

It splits the velocity budget evenly between distance-making and airtime; any other split shortens the product.

Does this include air resistance?

No — it's the ideal model taught in physics courses; real drag shortens and flattens the arc.