Projectile motion

Projectile Motion - Introduction

Projectile motion is an example of motion in two dimensions: a uniform horizontal motion and a uniformly accelerated vertical one (see the picture below). Notice, that the horizontal velocity vectors v_xhave the same direction and magnitude all the time. This is not the case for the vertical component of velocity, which changes due to the gravitational acceleration.

The trajectory of projectile motion is a parabola. The formula for the range of the projectile is

Experimental Procedure

The purpose of this lab is to verify the relationship between the range of the projectile and the launch angle. An additional exercise is to find the launch speed of the projectile.

Equipment

In this lab, you will use a mini launcher (Figure 1), with a protractor attached to it (Figure 2). You can control the launch speed (Figure 3) and the launch angle.

Figure 1. Mini Launcher

Figure 3. Launch Speed Control

Figure 2. Protractor

Figure 4. Launcher

In class, use the Short Range. Place the mini launcher at the edge of the table so the bullet can land on the floor. Adjust the angle, make sure that nobody is standing where the projectile should hit the floor, load the steel bullet (Figure 5), and launch the projectile (Figure 4).

Perform a couple of trial launches before taking any measurement.

Figure 5. Placing the ball in the launcher

Caution! Do not look down the barrel. Wear safety glasses when the launcher is in use.

To examine the relationship between the range and the launch angle, you need to perform two sets of measurements.

Horizontal projectile motion to find the speed of the projectile (Part 1),
Projectile at an angle to find the relationship between the range of a projectile and the launch angle (Part 2).

Part 1. Horizontal projectile motion

A ball launched horizontally has no initial vertical velocity. Thus, the time of flight can be determined based on the kinematic equation

h = gt²/2

Solve for t.

Knowing time and range, you can calculate the initial velocity

v = range/t

Set up the launcher as shown in Figure 6.

Figure 6. Horizontal projectile experimental setup with launcher

Perform at least five measurements for the short range. Report the average of your findings.

Part 2. Projectile at an angle

Set the experiment as shown in the figure below.

Figure 7. Range as a function of the launch angle experimental setup.

Set an angle. You can begin with 10 degrees, then 15, 20, 25, 30, and so on, up to 80.
Launch the projectile.
Measure the range.
Collect data in the provided table.

Analyses

Answer the following questions in the provided lab worksheet.

Which mathematical function represents the relationship between the range and the launch angle? What indicates that relationship in the range formula?
Plot the data. Put the angle on the horizontal axis and the range on the vertical one. Do the data points reflect the function from the first question?
What is the optimal angle for the maximum range?
What is the accuracy of the speed of the projectile?
What is the main source of error in this experiment? What parts of the experimental design need improvement?

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