Height Sets the Time, Speed Sets the Range
Two balls leave two ledges at the same instant. Give them the same height and different speeds and they land together but far apart; give them the same speed and different heights and the higher one is still in the air long after the other has landed. The two rules raced side by side, with every number from the lesson available as a preset.
Bu simülasyon nasıl kullanılır
- Press Same height, 2× speed to land two balls together at different distances
- Press Same speed, 4× height to see the fall times separate
- Load the worked example at 14.7 m/s from 19.6 m, or the relief-aircraft case
- Switch planets to change g and watch both the time and the range respond
Nelere dikkat etmeli
- Balls dropped from the same height always land at the same instant, whatever their speeds
- Doubling the launch speed exactly doubles the range and leaves the time untouched
- Quadrupling the height doubles the fall time and only doubles the range
- On the Moon everything takes far longer and travels correspondingly further
- Zero launch speed is just the dropped case, with the same time and no range at all
Arkasındaki fizik
For a horizontal launch the vertical motion starts from rest, so the fall time depends only on the height: t = √(2h/g). The horizontal motion is unaccelerated, so the range is whatever that time buys at the launch speed, x = v₀t = v₀√(2h/g). Height and speed therefore control different things — height owns the clock, speed owns the distance. Because the time enters the range through a square root, quadrupling the height only doubles the range, while doubling the speed doubles it exactly.