SOLUTION: A baseball is hit from a height of 0.8 m. After "t" seconds, its height "h", in metres, is given by the equation h=−5t2+20t+0.8. How long does the ball stay at least 15 m abo

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A baseball is hit from a height of 0.8 m. After "t" seconds, its height "h", in metres, is given by the equation h=−5t2+20t+0.8. How long does the ball stay at least 15 m abo      Log On


   

Question 1006685: A baseball is hit from a height of 0.8 m. After "t" seconds, its height "h", in metres, is given by the equation h=−5t2+20t+0.8. How long does the ball stay at least 15 m above the ground? (5 marks)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29+=+-5t%5E2+%2B+20t+%2B+.8+
I want to solve for +h%28t%29+%3E=+15+
+15+=+-5t%5E2+%2B+20t+%2B+.8+
+-5t%5E2+%2B+20t+-+14.2+=+0+
use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-5+
+b+=+20+
+c+=+-14.2+
+t+=+%28+-20+%2B-+sqrt%28+20%5E2+-+4%2A%28-5%29%2A%28-14.2%29+%29%29+%2F+%282%2A%28-5%29%29+
+t+=+%28+-20+%2B-+sqrt%28+400+-+284+%29%29+%2F+%28-10+%29+
+t+=+%28+-20+%2B-+sqrt%28+116+%29%29+%2F+%28-10+%29+
+t+=+%28+-20+%2B+10.7703+%29+%2F+%28-10%29+
+t+=+9.2297+%2F+10+
+t+=+.923+ sec
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and, also
+t+=+%28+-20+-+10.7703+%29+%2F+%28-10%29+
+t+=+30.7703%2F10+
+t+=+3.077+ sec
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The difference in these times is the time period
when +h%28t%29+%3E=+15+ m
+3.077+-+.923+=+2.154+
2.154 sec answer
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Here's a plot of the equation:
+graph%28+400%2C+400%2C+-1%2C+5%2C+-3%2C+25%2C+15%2C+-5x%5E2+%2B+20x+%2B+.8+%29+