SOLUTION: a rock is propelled upward from the top of a building 60 feet tall at an initial velocity of 200 feet per second. the function that describes the height of the rock in terms of tim

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Question 629186: a rock is propelled upward from the top of a building 60 feet tall at an initial velocity of 200 feet per second. the function that describes the height of the rock in terms of time t is s(t)=-16t^2+200+60. determine the time at which the rock reaches its maximum limit.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+s%28t%29+=+-16t%5E2+%2B+200t+%2B+60+
Find +t+ when +s%28t%29+ is a maximum
The maximum ( or minimum ) of a 2nd degree
equation of the form
+f%28x%29+=+ax%5E2+%2B+b%2Ax+%2B+c+ occurs at +x%5Bmax%5D+=+-b%2F%282a%29+
+a+=+-16+
+b+=+200+
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+t%5Bmax%5D+=+-200%2F%28-32%29+
+t%5Bmax%5D+=+6.25+
At +t+=+6.25+ sec, the height is a maximum
Here's a plot
+graph%28+400%2C+400%2C+-10%2C+20%2C+-30%2C+700%2C+-16x%5E2+%2B+200x+%2B+60+%29+