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A sniper fires a bullet perfectly horizontally off a clifftop. At the same instant, an identical bullet simply drops straight down from the same height. The fired one screams 800 m sideways; the dropped one lands at your feet. Which hits the ground first?
A sniper fires a bullet perfectly horizontally off a clifftop. At the same instant, an identical bullet simply drops straight down from the same height. The fired one screams 800 m sideways; the dropped one lands at your feet. Which hits the ground first?
They land at exactly the same moment — horizontal speed does nothing to fight gravity. See why, and you understand everything from a thrown football to a spacecraft trajectory.
In projectile motion, horizontal and vertical motions are completely independent. Gravity affects only the vertical motion; the horizontal velocity stays constant throughout (ignoring air resistance). Analyse each axis separately, then combine.
Both the fired and dropped bullets feel downward — horizontal speed is irrelevant to gravity, so they land together. Horizontal motion is uniform (no horizontal force); vertical motion is uniformly accelerated (constant downward pull). The 45° launch maximises range because and , the largest value sine takes — exactly why the sim's range peaked at 45°. **Limiting case:** is pure free fall up-and-down (range zero); maximises range; complementary angles () share a range because matches. **Connect it:** a projectile is two old laws glued at right angles — constant velocity sideways (no horizontal force, first law) and free fall vertically (second law) — running simultaneously and ignoring each other.
Thinking the horizontal and vertical motions affect each other — they are INDEPENDENT: gravity changes only the vertical motion while the horizontal velocity stays constant.