Question 277866
In 1981, Vadimir Poliakov (USSR) set a world record of 19ft ¾ in for the pole vault (www.polevault.com). To reach that height, Poliakov obtained a speed of approximately 36 feet per second on the runway. The formula h = -16t^2 + 36t gives his height t seconds after leaving the ground. 
a. Does the graph of this equation open up or down? How did you determine this?
Ans: Down because of the -16t^2
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b. Describe what happens to his height as time passes, starting at t=0?
Ans: h(0) = 0 means the height is zero when the time is zero.
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c. Use the method of your choice to find how long he was in the air.
Ans: Solve h=0 for two values of "t".
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d. Will his height peak or be at a low during the middle of the time he is in the air? How do you know?
Ans: peak because the parabola opens down and therefore has a peak at the vertex.
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e. After how many seconds will the peak or low occur?
Ans: Find the t-value of the peak at t = -b/2a
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f. How high will he be when the peak or low occurs?
Ans: Find h at that t-value.
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g. What is the point of the vertex? How does this number relate to your answers in parts e and f?
Ans: vertex has time of peak and height of peak.
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h. How many solutions are there to the equation 0 = -16t2 + 36t? How do you know?
Ans: It is a quadratic
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i. To use the quadratic formula to solve an equation like this, we need three values, represented in your text by a, b and c. In the equation in part h, what are a, b & c?
Ans a = -16 ; b = 36 ; c = 0
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j. What do the solutions to 0 = -16t2 + 36t represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?
Ans: They both tell the time when the vaulter is on the ground.
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Cheers,
Stan H.