We can make some relatively useful models using the math we have been studying.

Question

We can make some relatively useful models using the math we have been studying. For this project complete the following two models and answer the questions that follow. Your answers do not need to be typed, and you do not need to graph. We will work on this project Monday, November 6" in class. We will drop an object in class together. We will time how long it takes to hit the ground. Using the vertex form below make a model for the object drop. We will all have the same model. We will all have the same time for the obiect to hit the Use: H0)-16l-+ takes .6 Seconds on the model: What are the domain and range of our model? 2. 1. Why does the object never have a height of 100 feet? 3. Set your height equal to 100 feet and solve for x. 1, if someone were to grab the object when it was 3 feet from the after how many seconds would the person catch it? 5. According to our model how many seconds should it take for the object to hit the ground? 6. In reality how many seconds did it take the object to hit the ground? why are 5 and 6 different? Model 2 :Throw an object up model. Imagine that I am outside and I threw up the object up. Maybe at 1.0 second the ball had a maximum height of 20 feet. Answer the questions that below. 1. 2. 3. 4. 5. Write the equation of the object in vertex form. Assuming that I let go of the object at t-0, what was the object's initial height? Expand the vertex form into standard form to tell me the initial velocity (it is the b-term) When does the object hit the ground? What is the model's domain and range?

Explanation / Answer

Model 1

H(t) = -16(t - h)^2 + k

now, dropped from 9 ft

hence to model can be written as

H(t) = -16t^2 + 9

1. domain t = 0 to t = 0.69

range = 9ft to 0 ft

2. as the range of the model is not above 9 ft, the model never gives 100 ft from the output

also from the physical sense, a ball dropped from 9 ft can never reach 100 ft

3. 100 = -16t^2 + 9

t = sqroot(-5.6875) s

4. H(t) = 3

3 = -16t^2 + 9

t = 0.6123724 s

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