SOLUTION: The height (h) in feet of a person jumping off a diving platform can be modeled by the equation h=-16t^2+4t+6 where t represents the time in seconds the person is in the air. After

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The height (h) in feet of a person jumping off a diving platform can be modeled by the equation h=-16t^2+4t+6 where t represents the time in seconds the person is in the air. After      Log On


   

Question 1036506: The height (h) in feet of a person jumping off a diving platform can be modeled by the equation h=-16t^2+4t+6 where t represents the time in seconds the person is in the air. After how many seconds does the person jumping off the platform enter the water?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Person hits the water when height above
water is zero +h+=+0+
+h+=+-16t%5E2+%2B+4t+%2B+6+
+-16t%5E2+%2B+4t+%2B+6+=+0+
+-8t%5E2+%2B+2t+%2B+3+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-8+
+b+=+2+
+c+=+3+
+t+=+%28-2+%2B-+sqrt%28+2%5E2+-+4%2A%28-8%29%2A3+%29%29+%2F+%282%2A%28-8%29%29+
+t+=+%28-2+%2B-+sqrt%28+4+%2B+96+%29%29+%2F+%28+-16+%29+
+t+=+%28+-2+-+sqrt%28+100+%29+%29+%2F+%28+-16+%29+
+t+=+%28+-2+-+10+%29+%2F+%28+-16+%29+
( note that I chose the negative square root of +100+
so that time, t, would come out positive )
+t+=+%28-12%29+%2F+%28-16+%29+
+t+=+3%2F4+
After 3/4 sec, the person hits water
-------------------------------
here's the plot:
+graph%28+400%2C+400%2C+-1%2C+1.5%2C+-3%2C+12%2C+-16x%5E2+%2B+4x+%2B+6+%29+