In today’s class we launched an air-powered rocket using a bicycle pump to create air pressure in the launch cylinder of the rocket. The students used a stop watch to measure the rocket’s total flight time, from which they were able to calculate the rocket’s initial velocity and maximum height. We ignored air resistance in making these calculations. We repeated the experiment several times by varying the amount of air pressure in the launch cylinder. This gave different values for the initial velocity and maximum height of the rocket. Students learned that the greater the initial velocity leaving the launch pad, the greater the maximum height achieved by the rocket.
The formula for the rocket’s initial velocity is:
(initial velocity) = (1/2) * (acceleration due to gravity) * (total flight time)
At the Earth’s surface, the acceleration due to gravity is 9.8 m/s2. The longest recorded total flight time was 5.8 seconds, yielding an initial velocity of 28.4 m/s.
The rocket’s maximum height is given by
(maximum height) = (1/4) * (initial velocity) * (total flight time).
With a total flight time of 5.8 seconds and initial velocity of 28.4 m/s, the rocket’s maximum height was 41.2 meters.
After completing the calculations, we talked about the initial velocity necessary to escape the Earth’s gravitational pull: 11,000 m/s. We also talked about why real rocket’s do not leave the launch pad with such an enourmous velocity. The huge acceleration would be fatal to the astronauts!
Physics majors: You can derive the equations we used by starting with the kinematic equations, remembering that the rocket’s speed is zero at its maximum height. Remember also that we used the total flight time, since that was what we measured using the stop watches. The way the kinematic equations are ordinarily set up for max height calculations, t represents the time needed to reach maximum height (or to fall from maximum height), which is half of the total flight time.