Measuring the Velocity, Maximum Height and Angle of the Projectile

The Idea

This experiment will take you outside to make these measurements. You can also collect data from Monday night football.

The measurement part is very simple. All you need to measure is the total time a ball or other projectile is in the air and the total distance along the ground that the projectile travels. If we measure only those two things we can figure just about everything else: launch angle, velocity, and height.

How high did the punt go? How hard was the ball hit? What angle did it go? You kick a soccer ball, hit a golf ball, and punt a football. Which has the greater velocity? Without resorting to a high-tech solution, such as a radar gun, there is a simple way to answer that question using only the laws of motion.

To do this, you either work the calculations or use the tables as a guide—your choice.

What You Need

• stopwatch
• football field
• TV tuned to a football or baseball game
• assorted projectiles and launchers: soccer ball or football; tennis ball and racket; golf club and ball

Method

Projectile

1. Launch the projectile and, at the exact same time, start the stopwatch.
2. Record how far the object goes and how long it was in the air.

Calculation

If this section contains more math than you care to do, fast forward directly to the tables in the next section.

Figure 10-1 shows a punted football from the eyes of a physicist.

v_x = R/t

where g is 9.8m/s².

1. Find the horizontal velocity (in m/s), v_x, by dividing the overall distance, R, by the total time (hang time, t).
2. Find the vertical velocity (in m/s) by multiplying one half of the hang time (or the time to reach the peak) by the gravitational constant:
3. Find the velocity (in m/s) using:
4. Find the angle using:

(In case you don't know what tan^–1 is you can just use the key on your calculator with that identification. The function, tan^–1, also called the arctan, gives the angle if you have the tangent of that angle. You can get the tangent by dividing v_y by v_x.)

Find (or look up) the velocity, height reached, and angle launched.

Expected Results

See Tables 10-1 to 10-3.

Why It Works

This works for the same reasons as the previous experiment. Because horizontal and vertical motion are independent, the range and time in the air can uniquely be determined by the velocity, height, and launch angle.

Other Things to Try

Determine the velocity, maximum height, and angle for the following cases:

The results are shown in the following table:

The Point

Knowing only the time a projectile is in the air and the distance along the ground that it travels, it is possible to determine the velocity, maximum height, and angle of the projectile.

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