Launch a projectile at the same speed every time and change only the angle. It travels furthest at 45 degrees. Now the surprising part — launch at 30 degrees or at 60 degrees and the projectile lands in exactly the same place. But one of them stays in the air much longer than the other.
Choose Single or Pair at the top. In Single you fire one projectile at a time; turn on Keep trace and each completed flight stays on screen, up to twelve, so you can build the comparison yourself. In Pair, one angle slider fires both complementary angles at once. Set the speed with u and the angle with θ. Press Play to launch. Gravity is fixed at 10. Reset clears everything.
Before you launch, a faint arc shows where the projectile would go. Move the angle slider and that arc reshapes live — but nothing is fired until you press Play, so the class can predict first. The range measure is always on screen. Bring the angle within one degree of 45 and a maximum range label appears. In Pair mode the panel shows both flight times and both maximum heights side by side, and you can watch one ball land while the other is still in the air.
No air resistance. Launched from the ground and landing at the same level. In Pair mode you set one angle and the sim works out its complement — you cannot choose both.
Given one angle, you should be able to name the other angle that lands in the same place, and say which of the two gets there first.