Question 437300: 1. Suppose you are in the stands of a World Series baseball game. A foul ball is hit your way – you catch the ball, but in a moment of insanity (or too much beer), you throw the ball up in the air.
When a ball is thrown vertically upward from a height of 5 feet with an initial velocity of 96 ft/sec, its height can be modeled by a quadratic equation.
height=-16t^2+96t+5
a. Does the graph of this equation open up or down? How did you determine this? The ball graph of the equation opened down ward. I determined this because the coefficient of the highest power is negative.
b. Describe how the ball travels – what is the shape of its path? the path that the ball travels is upward into the air and bows slightly when returning downward.
c. Use the quadratic formula to determine how long it takes for the ball to land. Calculate to the decimal approximation for your answer.
Note. Your answer, t, will be in terms of seconds.
d. After how many seconds will the ball reach its maximum height?
e. What is the height that the ball will reach?
f. What is the point of the vertex of the quadratic equation? How does this number relate to your answers in parts d. and e?
g. How many solutions are there to the equation ? How do you know?
h. What do the solutions represent? Is there a solution that does not make sense? Why?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Suppose you are in the stands of a World Series baseball game. A foul ball is hit your way – you catch the ball, but in a moment of insanity (or too much beer), you throw the ball up in the air.
When a ball is thrown vertically upward from a height of 5 feet with an initial velocity of 96 ft/sec, its height can be modeled by a quadratic equation.
height=-16t^2+96t+5
a. Does the graph of this equation open up or down? How did you determine this? The ball graph of the equation opened down ward. I determined this because the coefficient of the highest power is negative.
b. Describe how the ball travels – what is the shape of its path? the path that the ball travels is upward into the air and bows slightly when returning downward.
c. Use the quadratic formula to determine how long it takes for the ball to land. Calculate to the decimal approximation for your answer.
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Solve: -16t^2+96t+5 = 0
t = [-96+-sqrt(96^2-4*-16*5)]/-32
t = [-96+-sqrt(9536)]/-32
Positive solution:
t = 6.05 seconds
Note. Your answer, t, will be in terms of seconds.
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d. After how many seconds will the ball reach its maximum height?
max occurs when t = -b/(2a) = -96/(2*-16) = 3 seconds
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e. What is the height that the ball will reach?
Solve for h(3)= 149 ft.
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f. What is the point of the vertex of the quadratic equation? How does this number relate to your answers in parts d. and e?
Ans: (3,149)
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g. How many solutions are there to the equation ? How do you know?
Ans: 2
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h. What do the solutions represent?
Time when the height of the ball is zero.
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Is there a solution that does not make sense?
Yes
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Why?
t is negative.
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Cheers,
Stan H.
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