SOLUTION: A football is kicked straight up into the air; it hits the ground 3.6s later.What was the greatest height reached by the ball? Assume it is kicked from ground level.

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Question 836334: A football is kicked straight up into the air; it hits the ground 3.6s later.What was the greatest height reached by the ball? Assume it is kicked from ground level.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If I say:
+h%28t%29+=+-16t%5E2+%2B+b%2At+
One of the roots is +t+=+0+
+h%280%29+=+0+
+0+=+-16%2A0%5E2+%2B+b%2A0+
and, the other root is:
+t+=+3.6+
+h%283.6%29+=+0+
+0+=+-16%2A3.6%5E2+%2B+b%2A3.6+
+0+=+-207.36+%2B+3.6b+
+3.6b+=+207.36+
+b+=+57.6+
-----------------
The maximum height is reached when:
+t%5Bmax%5D+=+-b%2F%282a%29+ where
+a+=+-16+
+b+=+57.6+
+t%5Bmax%5D+=+-57.6%2F%28-32%29+
+t%5Bmax%5D+=+1.8+
and
+h%28t%29+=+-16t%5E2+%2B+57.6%2At+
+h%281.8%29+=+-16%2A1.8%5E2+%2B+57.6%2A1.8+
+h%281.8%29+=+-51.84+%2B+103.68+
+h%281.8%29+=+51.84+
The greatest height reached is 51.84 ft
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+5%2C+-10%2C+60%2C+-16x%5E2+%2B+57.6x+%29+