SOLUTION: A toy rocket is launched from the top of a building 280 feet tall at an initial velocity of 112 feet per second. The height of the rocket t seconds after launch is given by the equ

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Question 954466: A toy rocket is launched from the top of a building 280 feet tall at an initial velocity of 112 feet per second. The height of the rocket t seconds after launch is given by the equation s(t)=-16t^2+112t+280. When does the rocket reach its maximum height? What is the maximum height?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+s%28t%29+=+-16t%5E2+%2B+112t+%2B+280+
When the form is:
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+, then
+x%5Bmax%5D+=+-b%2F%282a%29+
+a+=+-16+
+b+=+112+
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+t%5Bmax%5D+=+-112%2F%282%2A%28-16%29%29+
+t%5Bmax%5D+=+112%2F32+
+t%5Bmax%5D+=+3.5+
In 3.5 sec, the rocket is at maximum height
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+s%283.5%29+=+-16%2A3.5%5E2+%2B+112%2A3.5+%2B+280+
+s%283.5%29+=+-16%2A12.25+%2B+392+%2B+280+
+s%283.5%29+=+-196+%2B+392+%2B+280+
+s%283.5%29+=+476+
The maximum height is 476 ft
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check:
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+10%2C+-50%2C+500%2C+-16x%5E2+%2B+112x+%2B+280+%29+