SOLUTION: An arrow is launched upward with a velocity of 128 feet per second from the top of a 100-foot building. What is the maximum height attained by the arrow?

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Question 865782: An arrow is launched upward with a velocity of 128 feet per second from the top of a 100-foot building. What is the maximum height attained by the arrow?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +h%28t%29+ = the height of the arrow in feet
+h%28t%29++=+-16t%5E2+%2B+128t+%2B+100+
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This is a parabola of the form:
+y+=+ax%5E2+%2B+b%2Ax+%2B+c+
If the max height is at ( t[max], h[max] )
+t%5Bmax%5D+=+-b%2F%282a%29+
+a+=+-16+
+b+=+128+
+t%5Bmax%5D+=+-128%2F%28+2%2A%28-16%29%29+
+t%5Bmax%5D+=+4+
Plug this result back into equation to get +h%5Bmax%5D+
+h%5Bmax%5D++=+-16%2A4%5E2+%2B+128%2A4+%2B+100+
+h%5Bmax%5D+=+-256+%2B+512+%2B+100+
+h%5Bmax%5D+=+356+ ft
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Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+12%2C+-40%2C+450%2C+-16x%5E2+%2B+128x+%2B+100+%29+