Time of Flight, Height and Range
The time to the top comes from setting the vertical component to zero, and on level ground the flight lasts exactly twice as long — so the range is the horizontal component multiplied by that. Raise the launcher onto a 39.2 m roof and the doubling rule visibly breaks, which is precisely why the book attaches a condition to it.
इस सिमुलेशन का उपयोग कैसे करें
- Set the launch speed and angle and read the time, height and range together
- Load the worked example at 19.6 m/s and 30° — 1.0 s up, 2.0 s total, 34 m across
- Raise the launch height to 39.2 m and watch the doubling rule break
- Switch g between 9.8, 10, the Moon and Mars to rescale every result
क्या देखें
- On level ground the time up and the time down are exactly equal
- The range is largest at 45°, and 30° and 60° give the same range as each other
- Doubling the launch speed quadruples the range but only doubles the flight time
- From a raised launcher the descent takes longer than the ascent and the mirror rule fails
- Maximum height depends on the vertical component alone, so a steeper launch always goes higher
इसके पीछे की भौतिकी
The vertical component falls to zero at t_up = v₀ sin θ/g, giving a maximum height H = v₀²sin²θ/2g. On level ground the descent mirrors the ascent, so the total flight time is T = 2v₀ sin θ/g and the range is R = v₀ cos θ · T = v₀² sin 2θ/g — maximised at 45°, and equal for any pair of angles adding to 90°. The mirror argument relies on landing at the launch height. From a raised platform the fall is longer than the rise, T is no longer twice t_up, and the range formula fails.