SOLUTION: Suppose that a ball is projected upward from the top of the Mart Hotel in Dallas, Texas, which is 400 feet high. Its position s in feet above the ground is given by the equation &#

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Question 959507: Suppose that a ball is projected upward from the top of the Mart Hotel in Dallas, Texas, which is 400 feet high. Its position s in feet above the ground is given by the equation 𝑠=−16𝑡2+45𝑡+400. where t is the number of seconds elapsed.
a. How long will it take for the ball to reach a height of 200 feet above the ground?
b. When will the ball hit the ground? State the answer in number of seconds after the ball was projected.
c. What is the highest point that the ball reaches before falling back to earth? At what time will it reach that point?
Answer by lwsshak3(11628) About Me  (Show Source):
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Suppose that a ball is projected upward from the top of the Mart Hotel in Dallas, Texas, which is 400 feet high. Its position s in feet above the ground is given by the equation 𝑠=−16𝑡2+45𝑡+400. where t is the number of seconds elapsed.
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a. How long will it take for the ball to reach a height of 200 feet above the ground?
𝑠=−16𝑡2+45𝑡+400
200=−16𝑡2+45𝑡+400
−16𝑡2+45𝑡+200=0
solve for t with quadratic formula:
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=-16, b=45, c=200
ans:
t=-2.4 s (reject)
or
t=5.2 s
How long will it take for the ball to reach a height of 200 feet above the ground? 5.2 sec
..
b. When will the ball hit the ground? State the answer in number of seconds after the ball was projected.
Ball will hit the ground when height=0
−16𝑡2+45𝑡+400=0
Use quadratic formula to solve:
a=-16, b=45, c=400
ans: t=6.6 sec
When will the ball hit the ground? 6.6 sec
..
c. What is the highest point that the ball reaches before falling back to earth? At what time will it reach that point?
𝑠=−16𝑡2+45𝑡+400
complete the square:
s=-16(t^2-45/16+2025/1024)+2025/64+25600/64
s=-16(t-45/32)^2+2025/64+25600/64
s=-16(t-45/32)^2+29650/64
s=-16(t-45/32)^2+431.64
The ball reaches the highest point of 431.64 ft after (45/32)=1.4 sec