Projectile Motion: Trajectory, Range and Launch Angle

The two directions are independent. Nothing pushes the melon sideways, so its horizontal velocity never changes and the horizontal motion is constant velocity. Vertically, gravity removes 9.8 m/s of upward velocity every second, so the vertical motion is free fall. The range is just the horizontal speed multiplied by the time the melon spends in the air: R = v_0x · T. Raising the angle buys more hang time but spends horizontal speed to get it, and the range curve below is that trade-off drawn out. In dragon mode the melon has to arrive at a point in the air, not just at a distance along the ground, so the angle and the speed have to be chosen together — many pairs work, and finding one is the exercise.

Launched from the ground, the curve peaks at 45°, and any two angles that add to 90° share a range — 30° and 60° land in the same place, one on a low fast arc and one on a high slow one. That symmetry comes from returning to the launch height, so it breaks the moment the melon starts above the ground: from a cliff the extra fall time is worth more to a flat throw than to a steep one, and the best angle slides below 45°.

All of this assumes no air resistance, which is what AP Physics 1 projectile questions assume. The dragon is 7 m across and stands on the ground; the dashed ring is exactly the region counted as a hit — 1.1 m around its mouth, which sits 2.2 m up. The slice is treated as a point and the dragon does not move, so nothing about the strike itself is modelled: the sim answers only whether the path passes through that ring. The fire it breathes back after a miss is decoration and exerts no force — it is drawn only once the flight has already ended.