SOLUTION: A soccer ball is kicked from 3 feet about the ground. The height, h, in feet of the ball after t seconds is given by the function h=-16t2 + 64t + 3. Find the time it takes for the

Algebra ->  Expressions-with-variables -> SOLUTION: A soccer ball is kicked from 3 feet about the ground. The height, h, in feet of the ball after t seconds is given by the function h=-16t2 + 64t + 3. Find the time it takes for the       Log On


   

Question 1129111: A soccer ball is kicked from 3 feet about the ground. The height, h, in feet of the ball after t seconds is given by the function h=-16t2 + 64t + 3. Find the time it takes for the ball to return back to ground level. The answer should not be negative. Solve for t.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
At ground level, +h+=+0+
+-16t%5E2+%2B+64t+%2B+3+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-16+
+b+=+64+
+c+=+3+
+t+=+%28-64+%2B-+sqrt%28+64%5E2-4%2A%28-16%29%2A3+%29%29%2F%282%2A%28-16%29%29+
+t+=+%28-64+%2B-+sqrt%28+4096+%2B+192+%29%29%2F%28-32%29%29+
+t+=+%28-64+%2B-+sqrt%28+4288+%29%29%2F%28-32%29%29+
+t+=+%28+-64+-+65.4828+%29%2F%28-32%29+ ( I took the neg root to end up with positive time )
+t+-+%28+-129.4828+%29%2F%28-32%29+
+t+=+4.0463+ sec
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check answer:
Here's the plot:
+graph%28+600%2C+400%2C+-1%2C+6%2C+-5%2C+70%2C+-16x%5E2+%2B+64x+%2B+3+%29+