8. calculating velocity, acceleration, energy, force

If you are already familiar with mechanical equations you may have a go at calculating velocities and kinetic energies during impact. You will see that your graphs will be more useful than when you only recorded drop height.

The following equations will be helpful:

Impact Velocity: v_f = v_o + a·t, or:  v_f² - v_o² = 2·a·d

where v_f and v_o are final and original velocity, respectively, a is acceleration, t is time and d is distance travelled.

Kinetic Energy: E_k = 1/2 m·v²,

where m is mass and v is velocity.

Now you can make predictions about meteorite and asteroid impact velocities for real craters, by extrapolating your plots to larger diameters and shapes. Start with predictions that you can check with an experiment, e.g. predict a drop height for twice the diameter of your largest crater. First extrapolate your plot to the new crater dimensions and read the predicted drop height from your graph. Experiment until you have found the correct drop height and check if your prediction was correct. If it was not, what could have been the reason? Use your new insight in the next experiment.

Make a prediction for ‘real-life’ impacts. From a database of craters on Earth select a few examples of small and large craters. Estimate the impact energies and velocities for these craters. Find out on the Internet if your predictions are at least halfway realistic. Can you improve your predictions?