# Math

The International Space Agency is preparing an experiment to determine the acceleration of gravity on a planet. We know the height of a falling object (s) can be modeled by the equation s=1/2 at^2+v_o t+s_o, where a is the acceleration of gravity, vo is the initial velocity of the object, so is the initial height of the object, t is the time the object is in motion, and s is the height of the object. The experiment will use an altimeter and a timer to measure the height of a baseball that is thrown off a cliff. Use the data collected in the table to answer the questions.
Time (seconds) Height (meters)
0.5 108.0625
1 103.45
1.5 92.1625
2 74.2
3 18.25

What is the acceleration of gravity of the planet?
What was the initial velocity of the baseball?
From what altitude was the baseball thrown?
When did the baseball hit the ground?
When did the baseball reach the maximum height?

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1. all you have to do is solve y = at^2+bt+c given three points:
Let's use t=1,2,3
a+b+c = 103.45
4a+2b+c = 74.2
9a+3b+c = 18.25
h(t) = -13.35t^2 + 10.8t + 106

Now you can answer the questions.
It hits the ground when h=0
max height at the vertex: t = -b/2a

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posted by oobleck

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