Question 890666: When a basketball player shoots a ball from his hand at an initial of 2 m with an initial upward velocity of 10 meters per second, the height of the ball can be modeled by the quadratic expression -4.9t^2 + 10t + 2 after t seconds.
a. What will be the height of the ball after 2 seconds?
b. How long will it take the ball to reach the height of 4.5 m?
How long will it take to touch the ground?
c. Do you think the ball will reach the height of 12 m? Why?
d. Will the ball hit the ring if the ring is 3 m high?
e. Write a similar situation with varied initial height when the ball is thrown with an initial upward velocity. Then model the path of the ball by quadratic expression.
f. Using the equation and the quadratic expression you have written in item e, formulate and solve problems involving the height of the ball when it is thrown after a given time.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! When a basketball player shoots a ball from his hand at an initial of 2 m with an initial upward velocity of 10 meters per second, the height of the ball can be modeled by the quadratic expression -4.9t^2 + 10t + 2 after t seconds.
a. What will be the height of the ball after 2 seconds?
h(t) = -4.9t^2 + 10t + 2
Sub 2 for t
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b. How long will it take the ball to reach the height of 4.5 m?
h(t) = -4.9t^2 + 10t + 2 = 4.5
Solve for t
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How long will it take to touch the ground?
h(t) = -4.9t^2 + 10t + 2 = 0
Solve for t
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c. Do you think the ball will reach the height of 12 m?
The max height is the vertex of the parabola.
The vertex is on the axis of symmetry, t = -b/2a = -10/-9.8
Max ht is at 50/49 seconds
h(t) = -4.9t^2 + 10t + 2
Sub (50/49) for t for max ht.
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Why?
d. Will the ball hit the ring if the ring is 3 m high?
Depends on the max ht above.
h(t) give the height of the center of the ball, take that into account.
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e. Write a similar situation with varied initial height when the ball is thrown with an initial upward velocity. Then model the path of the ball by quadratic expression.
h(t) = -4.9t^2 + 10t + ho (ho = initial height)
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f. Using the equation and the quadratic expression you have written in item e, formulate and solve problems involving the height of the ball when it is thrown after a given time.
Same as above
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