Projectile

About the Projectile game

Projectile motion is the first real engineering model most students meet in physics: throw something, ignore the air, and its path is a parabola you can predict on paper. This Projectile game turns that model into ten target levels. You pick a launch angle and a launch speed, press Fire, and the ball flies under gravity with g = 9.81 m/s². After every shot the panel under the field works the equations with your numbers, so you can see why the ball fell short or flew long. It is meant for civil and mechanical engineering students revising kinematics, and for anyone who likes a clean shot.

Levels add a wall to clear, a target on a rooftop, a launch from a cliff, and carts that roll back and forth. The simulation plays at twice real speed so long flights do not drag; the times shown are the true flight times.

How to play Projectile

1. Read where the target is from the grid. Lines are 10 m apart and every distance is in metres.
2. Set the angle θ and speed v with the sliders, or click the field and use the arrow keys: Up and Down for angle, Left and Right for speed, Shift for bigger steps.
3. Press Fire or Space. The ball must drop into the basket from above to count.
4. Read the working, adjust, and fire again. After three misses a hint gives the speed needed at your current angle.
5. Hit the target to unlock Next level. Your fewest shots for each level are kept on this device.

The equations used

The launch velocity splits into a horizontal part vₓ = v cos θ, which never changes, and a vertical part v_y = v sin θ, which gravity reduces by 9.81 m/s every second. The position after time t is x = vₓ t and y = h₀ + v_y t − ½ g t². The highest point is H = h₀ + v_y² / 2g. On flat ground the range is R = v² sin 2θ / g, which is largest at 45°, and two angles that add up to 90° give the same range. From a cliff of height h₀ the flight time is T = [v_y + √(v_y² + 2g h₀)] / g.

Low shot or high lob

For most targets there are two angles that work at one speed: a flat fast shot and a high slow lob. Walls force the lob. A moving cart rewards the flat shot, because a shorter flight gives the cart less time to move. Real shells, balls and water jets lose speed to air drag, so real ranges are shorter than this model says; that correction is a topic for a later fluid mechanics course.