Air Rockets

Purpose

The object of today’s exercise is to test the independence of the horizontal and vertical components of motion for freely falling bodies. You will launch air rockets vertically, and use information about the vertical motion to predict how far horizontally the rocket will go when fired at an angle. We’ll conclude with a contest to see which group can predict most accurately where their rocket will land.

Theory

As pointed out in the lab theory discussion for projectile motion, under the influence of gravity alone, an object will accelerate downward only. Not only that but, regardless of the mass of the object, it will accelerate at a constant 9.8 m/s² downward. However, since gravity only acts downward, the horizontal velocity will remain constant in the absence of other forces (e.g., air resistance). The horizontal and vertical components of motion for freely falling bodies are completely independent, so we can calculate the two separately.

Restated here are the basic equations for projectile motion in two dimensions. There are three equations for each dimension, and they show how the position, velocity, and acceleration of the object depend on time and the initial velocities in the x direction and the y direction.

Position:

Velocity:

Acceleration:

We will determine the initial velocity of the rocket by timing it when launched vertically. In this case, the x velocity is zero, and the total initial velocity is just the value of the initial velocity in the y direction. We’ll measure the total time it takes to go up and come back down, and also measure the time it takes to reach the top of its flight. The first method may introduce some error as the rocket is likely to tumble on the way back down, increasing its air resistance and slowing its fall slightly. The second method involves estimating when it reaches its peak, which can be tricky for the higher powered caps. Using both methods gives us an extra check on the reliability of the data.

Since the velocity is zero at the top of the peak, we can use the second equation for the y component to determine the initial velocity given the time to reach the peak (or half the total time of flight).

, or

The initial velocity should remain the same if the rocket is launched at an angle, since this is just based on the amount of pressure built up. However, although the total velocity will be the same, some of this will be directed upward and some of it will be directed horizontally. You can determine the component velocities from the angle of launch. From the new vertical velocity, we can determine how long it should take the rocket to reach its peak and come back down. Then, we can use this time and the horizontal velocity to detemine how far the rocket will travel.

Experimental Procedure

1. Set up the launch stand. Try to aim the rocket as close to verticle as possible. Any angle can affect your initial velocity measurements.

2. Fit the cap over the top of the stand. Begin by using the lowest power blast cap (Low); we’ll work our way up the ladder. Place the rocket over the stand and cap assembly.

3. Attach the bicycle pump to the nozzle at the bottom of the rocket assembly. Reset the timer and be ready to start it. If you use two timers, you can take both measurements from a single launch.

4. Pump the bicycle pump to launch the rocket. Start the timer as soon as it launches.

5. Record the time to reach the peak altitude and the total time of flight for three separate launches.

6. Repeat for each of the sizes of blast caps.

		Cap Power
		Low	Medium	High	Super
Time to Peak (tpeak)	trial 1
	trial 2
	trial 3
	average
Total Time (ttot)	trial 1
	trial 2
	trial 3
	average
v0 = gtpeak
v0 = gttot/2
v0 (average)

7. Calculate the initial velocity based on each of these methods, and then average them. Or, if based on your measurements, you think one method or the other was significantly more reliable, you can choose to just use that one and ignore the other.

8. Select an angle to launch a rocket for each of the cap sizes (you can choose the same or different angles for each). Based on the initial velocity and launch angle, calculate the vertical and horizontal components of the velocity, the total time aloft, and predict the total horizontal distance travelled.

Cap Type	v0	θ	vy0 = v0 sinθ	vx0 = v0 cosθ	tf = 2 vy0/g	xf = vx0tf
Low
Medium
High
Super

9. Now that you have a prediction for the distance, we’ll test your accuracy. Set out a target at the distance you predicted. The simplest method for longer distances is probably to measure the length of someone’s pace and then pace out the distance. Make sure you have the rocket aimed carefully so that you don’t miss to the left or right. Time the flight to compare the travel time with your prediction, and we’ll measure the distance from your predicted landing point.

Cap Type	tf predicted	tf observed	distance from target
Low
Medium
High
Super

Questions

Did the rocket take about the predicted amount of time to land?

What might be reasons why you didn’t hit the target exactly?

Which blast cap landed closest to your predicted target?

If you used different launch angles, for which one was the prediction most accurate?

Do you think our claim that the vertical and horizontal motion can be calculated independently is reasonable?