Problema Solution
A bag of sand was tossed from the top of a building where h(t)- Height is a function of t- Time. The following data points are recorded in the experiment.
t .3 .9 1.8 2.7
h(t) 13.791 11.319 7.476 3.471
a. Find the equation that models this data
b. How tall was the building that the sand was thrown from?
c. How long did it take for the bag to hit the ground?
d. Determine the practical domain of this experiment.
e. Determine the practical range of this experiment.
Answer provided by our tutors
The height of an item falling can be modeled by
h(t) = -16t^2 + h0,
where h0 is the initial height in feet at time t in seconds
We will use the fact that for t = 0.3 we have h(t) = 13.791
h(0.3) = -16*0.3^2 + h0
-16*0.3^2 + h0 = 13.791
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click here to see all the equation solution steps
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h0 = 15.231
h(t) = -16t^2 + 15.231
a. The equation that models this data is: h(t) = -16t^2 + 15.231
b. How tall was the building that the sand was thrown from? h0 = 15.231 ft
c. How long did it take for the bag to hit the ground?
h(t) = 0
-16t^2 + 15.231 = 0
........
e. Determine the practical range of this experiment.
[0, 15.231]