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Question 394941: When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -5t^2 + v*t + k gives the height of the ball at any time, t in seconds, where “v” is the initial velocity (speed) in meters/sec and “k” is the initial height in meters (as if you were on top of a tower or building).
Make up a scenario where a ball is thrown, shot, etc. into the air. You can choose any initial velocity (in meters/sec) and any initial height (in meters) of the ball, but include them in your written scenario. The ball can leave your hand, the top of a building, etc. so you can use many different values for the initial height.
1.Insert the chosen values for “v” and “k” into the formula listed above.
2.Use the formula to find the height of the ball at any two values of time, t, in seconds that you want. Show your calculations and put units on your final answer!
3.Provide a written summary of your results explaining them in the context of the original problem.
Please make sure that your answers make sense!
my scenario is: my 11 year old son holds his footballin his hand around 4 feet, he threw the ball up and outward towards his brother which took two seconds to get to him at the highest height of 20feet
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! my scenario is: my 11 year old son holds his footballin his hand around 4 feet, he threw the ball up and outward towards his brother which took two seconds to get to him at the highest height of 20feet
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Formula for height of the ball at time = t seconds.
h(t) = -16t^2+vot+so where vo is the initial velocity of the object
and so is the height (in feet) at which the object is thrown.
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Solve:
20 = -16(2^2)+vo(2)+4
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16 = -64 + 2vo
80 = 2vo
vo = 40 ft/sec
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Comment:
This is what your problem statement says:
Make up a scenario where a ball is thrown, shot, etc. into the air. You can choose any initial velocity (in meters/sec) and any initial height (in meters) of the ball, but include them in your written scenario. The ball can leave your hand, the top of a building, etc. so you can use many different values for the initial height.
1.Insert the chosen values for “v” and “k” into the formula listed above.
2.Use the formula to find the height of the ball at any two values of time, t, in seconds that you want. Show your calculations and put units on your final answer!
3.Provide a written summary of your results explaining them in the context of the original problem."
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Comment: You are supposed to provide an initial velocity and initial
height and then find the time.
So let vo = 40 ft/sec and let so = 4 ft. Then solve for the height
of the ball at 1 sec and again at 2 seconds.
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h(t) = -16t^2+40t+4
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h(1) = -16+40+4 = 28 ft
h(2) = -16(4)+40(2)+4 = 20 ft
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Hope this helps.
Cheers,
Stan H.
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