Rocket science and orbit simulation for hobbyists: The motion of falling bodies

Falling bodies

and Their Motion

This page originally compiled Feb 2007 by TFR

Falling bodies are a good example of what we have already called uniformly accelerated motion. Of course, objects can fall onto any planet in the solar system, but we will limit our discussion to bodies falling to the Earth. The acceleration under the force of the Earth's gravity, a constant called g, is well known. At sea level, it amounts to 32.2 feet/sec or 980 cm/sec, approximately. This value varies with altitude, but for our first approximation we will assume it constant, and we will neglect the interference with gravitational motion caused by our object passing through the Earth's atmosphere.

We have already learned that
    s = (v_f² - v₀²) / 2a
    t = (v_f - v₀)/a
If we substitute g for a in the above equations we can simulate a falling body. Let us solve for the final velocity, v_f:
    v_f = √ v₀² + 2as,   or   v_f = √ v₀² + 2gs,   and,
    t = (v_f - v₀)/g
Examples:
    A rock falls from the top of a cliff 150 meters high. At what velocity does it hit the ground below?
        v_f = √ 0 + 2 × 9.80 × 150     = 54.2 m/sec   = 195 km/hr
        How long does it take to reach the ground?
        t = (54.2 - 0)/9.80   = 5.5 seconds
    A parachutist jumps from an airplane at 5000 feet. If Earth had no atmosphere, at what velocity would he hit the ground?
        v_f = √ 0 + 2 × 32.2 × 5000     = 567 ft/sec   = 387 mi/hr
        How long would he have to think about the fact that an airplane could fly with no atmosphere?
        t = (567 - 0)/32.2   = 17.6 seconds

Home

Last Revised: Feb 2007