Download Stomp Rockets Activity

Stomp Rockets!
Projectile motion and Quadratic Equations
Step 1 - Launch the rocket.
Today your group will launch a stomp rocket and calculate an equation for its trajectory.
The launching apparatus should be set to launch at a 45° angle. That is the lowest angle with the ground
that the launcher will allow.
Launch the rocket so that it travels parallel to the sideline of the field.
Take a couple trial launches if needed but then you will need to record two pieces of data for your
official launch:
Distance travelled _____________________ (yards)
Time in flight _________________________(seconds)
You should record your results with one decimal place of precision.
Step 2 - How high did the rocket go?
Because the pull of gravity that brings the rocket back down to Earth is constant, we have a function
that will tell us the maximum height of the rocket as a function of the time in flight.
Height (in yards) = f(t) = 5.36 (t/2)2
The physics background on that equation…
= ½ g t2
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Vertical distance in free fall is given by d
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In this equation, g represents the acceleration due to gravity and 5.36 yards/sec2 is equal to
½ gravity on Earth. (Most students are used to seeing this in m/s2, but since we are on a
football field measured in yards, we will also consider gravity using yards.)
We use half the time (t/2) since we only want to consider the time falling, not also going up.
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Use the formula to calculate the maximum height for your rocket.
Maximum height = _______________________ (yards)
Step 3 - Plot the trajectory of your rocket.
Sketch a graph that shows the trajectory of your rocket.
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The x-axis should show distance travelled. (You started at distance zero.)
The y-axis should show the altitude of the rocket.
While the graph will be a sketch, you should be able to accurately mark the starting point, the
ending point and the highest point (vertex) of the trajectory.
The vertex occurs midway between the launch and landing points.
The shape of the graph should be a parabola.
Be sure to label your axes!
Step 4 – Determine the concavity of the trajectory.
Is the concavity of the rocket’s trajectory up or down? ______________________
While your choice of concavity was (probably) easily made from your graph, justify your choice by
discussing the change in the rate at which the rocket is climbing and falling.
Step 5 - Find the equation of the trajectory.
The shape of the trajectory was a parabola, so we expect to get a quadratic equation to model the flight.
Since the starting and ending points of the trajectory are both on the x-axis, they are the roots of the
equation.
Height is a function of the distance travelled:
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h(x) = y = a(x-r)(x-s)
In this equation ‘r’ and ‘s’ are the x-intercepts, and ‘a’ is a constant.
Plug in your ‘r’ and ‘s’ values (one should be zero, the other the distance travelled.)
Plug the (x,y) coordinates of the vertex into the equation to calculate the value of the constant,
‘a’.
Show your work and write down your equation.
Trajectory equation (height as a function of distance) __________________________________
Step 6 - Convert your equation to standard form.
The standard form for a quadratic equation is:
y = Ax2 + Bx + C
This form of the equation has coefficients that can be used with the quadratic formula to solve the
equation (when it is set equal to zero.)
Convert your equation from step 5 into standard form by multiplying the factors (show your work!)
Equation in standard form _________________________________________
Step 7 - Use your equation to predict where you should stand
to make the rocket go through a hoop.
What is your height _________________(inches)
There are 36 inches in 1 yard…
What is your height _________________(yards)
You are going to calculate at what distance from the launcher the rocket will be at the same height as
you. There are actually two points at which this will be true. We would like to find the distance as the
rocket is coming down, rather than going up.
Using your equation from step 6, solve for the distance at which the rocket is at your height. Use the
quadratic formula. You can look at your graph to check your result.
Show your work!
Distance________________ (yards)
Step 8 - Actually try it!
Hold the hoop to the side of you so that the center of the hoop is even with the top of your head.
Launch the rocket with the same force as before.
Watch the rocket go through the hoop! (You may need to move laterally if the shot is not straight.)
Caution: The trajectory of a launched stomp rocket can vary quite a bit from trial to trial. There’s a
good chance this won’t work just because this launch is stronger or weaker than the one you have
calculated with. However if the rocket lands at about the same distance as before – the rocket should
go through the hoop!
Write a few sentences telling what happened in your trial(s).