Part (a)
t = time in seconds
h(t) = height of the rocket
The general projectile equation is
h(t) = -16t^2 + vt + k
where v is the starting or initial velocity (in this case v = 64) and k is the starting height (k = 0 in this case)
Therefore, the equation is h(t) = -16t^2 + 64t
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Part (b)
See graph below. I recommend using your graphing calculator or some online free tool to get the job done. Doing this by hand would be a pain and it could lead to inaccuracies. I used GeoGebra to make the graph.
To get it done by hand, you basically plug in various t values to find corresponding h(t) values. This leads to generating points in which you draw a parabolic curve through them all.
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Part (c)
The graph from part (b) shows that the highest point is at (2,64), which is where point B is located.
This means that after t = 2 seconds, the largest height is reached at h(t) = 64 feet.
The rocket then takes another 2 seconds to go from the highest point back down to the ground.
The total time the rocket is in the air is 4 seconds. We could double the value t = 2, or note the distance between A and C on the x axis.
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Answers:
- max height = 64 feet
- time it takes to reach max height = 2 seconds
- total time rocket is in the air = 4 seconds