MM212 Human Cannonball Unit 8 Discussion
Human Cannonball
Post 1: Initial Thread
The graphs of quadratic equations are parabolas (U-shaped), and solving a quadratic equation can tell you where a curve crosses the x-axis (by finding the “zeros” of the equation). The following quadratic equation represents a projectile in motion. The projectile is you! You are being shot out of a cannon. Use the following equation to determine how many seconds it will take for you to hit the ground.
Y is your height in feet off of the ground at any time during your “flight,” v is your initial velocity in feet per second, h is your starting height in feet off of the ground, and t is time in seconds.
- Choose values for the variables using the following parameters. Your cannon must be at least 10 feet off the ground but no more than 30 feet. The initial velocity can be anywhere from 75 to 150 feet per second.
- Since you want the time required for you to land (safely!) on the ground, let your height, Y = 0. Substitute the values into the equation and calculate the time, t, you will be flying through the air. Remember that you may calculate possible solutions that do not make sense. How long will you be flying through the air? (Note, for this discussion, you do not need to show each step in your calculations.)
- Graph the parabola of your equation at this Desmos calculator. Note that time, t, is the horizontal x-axis, and height, y, is the vertical y-axis. Graph the parabola and take a screenshot of the graph. Make sure the value at the point where you hit the ground (x, 0) is clearly shown. Save your screenshot as a picture and embed in your post. Note: there is a video in the Unit 8 LiveBinder that will show you how to embed a picture in your post.
- Using the graph, estimate the vertex, x- and y- intercepts. Share these points as an ordered pair (x,y). (Note there may be more than one intercept.)
- Explain what the vertex, x- and y-intercepts mean in the situational context, in terms of how high you, the human cannonball, fly and also the time that you are flying.
Post 2: Reply to a Classmate
Choose one classmate’s post that you find interesting and reply to their post.
- Calculate how high, Y, they are at time, t = 1, 5, and 10 seconds. Show all steps in your calculations.
- Do the answers make sense? Why or why not? Explain.
Post 3: Reply to Another Classmate
Find another classmate’s post that has a Post 2 response. Read the conversation thread and consider the parabola in Post 1 and the calculations in Post 2.
- How are the calculated heights at t = 1, 5, and 10 seconds of Post 2 represented on the parabola of Post 1? Explain in several sentences.
- List any calculated heights that fell below the x-axis (underground).
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MM212 Human Cannonball Unit 8 Discussion Answer
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