SOLUTION: A diver bounces off a 3 m springboard at an initial upward speed of 4 m/s. Over what time interval is the height of the diver greater than 3.5 m above the water? Round to the neare

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A diver bounces off a 3 m springboard at an initial upward speed of 4 m/s. Over what time interval is the height of the diver greater than 3.5 m above the water? Round to the neare      Log On


   

Question 1131410: A diver bounces off a 3 m springboard at an initial upward speed of 4 m/s. Over what time interval is the height of the diver greater than 3.5 m above the water? Round to the nearest hundredth of a second.
h = -4.9t^2 + 4t + 3
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h+=+-4.9t%5E2+%2B+4t+%2B+3+
+h+=+3.5+
+3.5+=+-4.9t%5E2+%2B+4t+%2B+3+
+-4.9t%5E2+%2B+4t+-+.5+=+0+
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-4.9+
+b+=+4+
+c+=+-.5+
+t+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A%28-4.9%29%2A%28-.5%29+%29%29%2F%282%2A%28-4.9%29%29+
+t+=+%28-4+%2B-+sqrt%28+16+-+9.8+%29%29%2F%28%28-9.8%29%29+
+t+=+%28+-4+%2B-+sqrt%28+6.2+%29+%29%2F%28-9.8%29+%29+
+t+=+%28+-4+%2B+2.49+%29%2F%28-9.8%29+
+t+=+%28-1.51%29%2F%28-9.8%29+
+t+=+.154+
and, also:
+t+=+%28+-4+-+2.49+%29%2F%28-9.8%29+
+t+=+.662+
The height is greater than 3.5 m above the water
between .154 sec and .662 sec
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Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+2%2C+-1%2C+4%2C+-4.9x%5E2+%2B+4x+%2B+3+%29+
Looks like the answers could be right. Check the math.