Projectile motion SIM

Projectile Motion - Introduction

Projectile motion is an example of motion in two dimensions: a uniform horizontal motion and uniformly accelerated vertical one (see the picture below). Notice, that the horizontal velocity vectors v_x have 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. In the picture below

v_y0 > v_y1 > v_y2 > v_y3

v_y3 = 0

v_y3 < v_y4 < v_{y5 <} v_y6

_{Notice also that}

|v_y0| = | v_y6|, _|v_y1| = | v_y5|, and _|v_y2| = | v_y4|;

v_y0 , v_y1, and v_y2 are upward, but v_y4, v_y5 , and v_y6 are downward.

At the same time

v_x0 = const.

As shown in the picture, the trajectory of projectile motion is a parabola.

Projectile motion trajectory - computer lab

Use Projectile motion trajectory - computer lab by Andrew Duffy to examine the relationship between the maximum height and range vs. the launch speed and angle. The link open a simulation of projectile motion.

The accepted gravity value for this sim is 10 m/s². Both range (x) and max. height is shown for each launch (Figure 1). The motion trajectory is shown as a purple line (Figure 2).

You can control the launch speed (Figure 3) and angle (Figure 4). Adjust both to the desired values, then press "Play" (Figure 5).

After taking notes, reset the sim. Repeat to fill out the tables in your Lab Report (see the Experimental Procedure below).

Experimental Procedure

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

1. Examine changes in the maximum height and range values when you change the launch speed for a fixed angle value (Part 1),

2. Examine changes in the maximum height and range values when you change the launch angle for a fixed speed value (Part 2).

Part 1. Maximum height and range values as a function of the launch speed for a fixed angle

1. Choose an angle for your experiment. Note it.

2. Set the launch speed at 10 m/s. Launch the projectile ("Play"). Write down the range (x) and the maximum height (max. height). Repeat for 11 m/s, then for 12 m/s, and so on through 25 m/s.

3. Collect the data in a table as show below.

Plot the data collected in both tables (you will plot TWO separate GRAPHS). You can plot the graphs in Excel and submit the spreadsheets or in Desmos and send the links to the instructor. It is a good practice to save your work (does not matter whether you work in Excel or in Desmos) so you can fix it later if necessary without typing all the coordinates once again.

Part 2. Maximum height and range values as a function of the launch angle for a fixed speed

1. Choose the launch speed for your experiment. Note it.

2. Set the angle at 5⁰. Launch the projectile ("Play"). Write down the range (x) and the maximum height (max. height). Repeat for 10⁰, then for 15⁰, and so on through 90⁰.

3. Collect the data in a table.

Plot the data collected in both tables (you will plot TWO separate GRAPHS). You can plot the graphs in Excel and submit the spreadsheets or in Desmos and send the links to the instructor. It is a good practice to save your work (does not matter whether you work in Excel or in Desmos) so you can fix it later if necessary without typing all the coordinates once again.

Plot the data and send to the Dropbox.

Analyses

Which mathematical function represents the relationship between the range and the launch speed in projectile motion? What indicates that relationship in the range formula?

Which mathematical function represents the relationship between the range and the launch angle in projectile motion? What indicates that relationship in the range formula?

What is the optimal angle for the maximum height?

What is the optimal angle for the maximum range?