Projectile Motion
Department of Physics and Astronomy
59
Projectile Motion
Pre-lab Assignment
Derive algebraic expressions for the range and total time-of-flight of a projectile launched with
initial speed vo from a height h at an angle
above horizontal.
Hint: The simplest method to derive these equations is to make use of the kinematic equations of
motion in both the x (horizontal) and y (vertical) directions. Consider making the origin of your
coordinate system the point from which the ball is launched, label it (xo, yo) and label the final
position of the ball as (x, y). Assign the downward vertical direction as negative (so that the
acceleration is a = -g = -9.8 m/s2), and note that the y-component of the initial velocity is +vosin.
Once you know the total time-of-flight, the horizontal range, R, is easy to find.
Pre-lab Questions and Exercises
1. Use the equations derived above to predict where the landing pad should be placed for a
typical projectile launched with an initial speed of 3.2 m/s from a height of 1.2 m at an angle
of 30 degrees. What will be the time of flight for this scenario?
2. What are the most likely sources of uncertainty in this experiment? How will you account for
these factors?
3. Set up an Excel spreadsheet to calculate the range and time-of-flight using the equations
derived above. Vary each of the input parameters by 10% and examine the differences in the
calculated results. Use this analysis to rank the sensitivity of the three parameters and predict
the primary source of uncertainty for this experiment.
4. Why should the launch angle be zero when measuring the initial speed of the ball in Part 2?
What would be the consequence of measuring the initial speed at a launch angle of 30º?
Introduction
In this lab you will study the motion of a freely-falling projectile, namely a small plastic sphere.
Projectile motion, for our purposes, is the motion of an object that has been launched and then is
subject to only the force of gravity and the force of air friction. The Newtonian mechanics principles
that you have been studying allow you to predict this type of motion quite well. You will perform two
experiments to aid your understanding of these principles, which will be described later in the lab.
Since there is the small but real possibility of causing injury to yourself or another person, please
follow all safety guidelines and common sense safety rules.
