SOLUTION: A ball falls from the top of a roof 320 feet above the ground. The formula h = -16t2 + 16t + 320 described the height of the ball above the ground, h, in feet, t seconds after the

Algebra ->  Equations -> SOLUTION: A ball falls from the top of a roof 320 feet above the ground. The formula h = -16t2 + 16t + 320 described the height of the ball above the ground, h, in feet, t seconds after the      Log On


   

Question 345461: A ball falls from the top of a roof 320 feet above the ground. The formula h = -16t2 + 16t + 320 described the height of the ball above the ground, h, in feet, t seconds after the fall begins. How long will it take the ball to strike the ground?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When the ball hits the ground, h+=+0, so
+h+=+-16t2+%2B+16t+%2B+320+
+0+=+-16t2+%2B+16t+%2B+320+
Divide both sies by 16
-t%5E2+%2B+t+%2B+20+=+0
Use quadratic equation to find t
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+-1
b+=+1
c+=+20
t+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A%28-1%29%2A20+%29%29%2F%282%2A%28-1%29%29+
t+=+%28-1+%2B-+sqrt%28+1+%2B+80+%29%29%2F%28-2%29+
t+=+%28-1+%2B-+sqrt%28+81+%29%29%2F%28-2%29+
Take the negative square root in order
to get a positive answer:
t+=+%28-1+-9%29%2F%28-2%29
t+=+10%2F2
t+=+5 sec
The ball will hit the ground in 5 sec
check answer:
-t%5E2+%2B+t+%2B+20+=+0
-5%5E2+%2B+5+%2B+20+=+0
-25+%2B+5+%2B+20+=+0
0+=+0
OK