Time to Fall

Introduction

Drop an object from a measured height and time how long it takes to land, then repeat from several different heights. Height and time to fall are related by a power law, not a straight line, so plotting them directly gives you a curve. Taking logarithms of both height and time straightens that curve out, and the gradient of the resulting line tells you the power in the relationship. From the same data you can use calculus to work out the object's velocity at any point during the fall, and start asking where air resistance would begin to matter.

Guiding Questions

• Drop an object from several different heights and time the fall for each. How could you improve the accuracy of your timing?
• Plot height against time to fall. What shape do you expect the curve to have, and does your data match it?
• Take logarithms of both height and time and re-plot. Does a straight line come out, and what does its gradient tell you about the relationship between height and time?
• Use calculus to find the velocity of the falling object from your height-time model. How does it compare with what a stopwatch and a speed sensor would measure?
• Where does the simple model stop matching reality — for a lighter object, or a larger one, where air resistance matters more?