Question 87464: Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
• 16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
a) What is the function that describes this problem?
Answer: quadratic function
b) The ball will be how high above the ground after 1 second?
Answer:
Show work in this space.
c) How long will it take to hit the ground?
Answer:
Show work in this space.
d) What is the maximum height of the ball?
Answer:
Show work in this space.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
• 16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
a) What is the function that describes this problem?
Answer: s(t) = -16t^2+32t
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b) The ball will be how high above the ground after 1 second?
Answer: s(1) = -16(1)^2 + 32*1 = 16 ft.
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c) How long will it take to hit the ground?
Answer:
Show work in this space.
Let s(t) = 0 (this is the height when the ball is on the ground)
-16t^2+32t = 0
-16t(t-2) = 0
t = 0 or t=2
On the ground at t=0 seconds and at t = 2 seconds.
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d) What is the maximum height of the ball?
Answer:
Show work in this space.
Max height is the s-coordinate of the vertex.
The max occurs when t = -b/2a = -32/2(-16) = 1 second
As you saw above s(1) = 16 ft which is the maximum height.
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Cheers,
Stan H.
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