SOLUTION: show all work for the following math problem: Annie Pelletier won a bronze medal in the wonmen's spring board competition at the 1996 olympics in atlanta.She somersaults from a 3-m

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: show all work for the following math problem: Annie Pelletier won a bronze medal in the wonmen's spring board competition at the 1996 olympics in atlanta.She somersaults from a 3-m      Log On


   

Question 285385: show all work for the following math problem: Annie Pelletier won a bronze medal in the wonmen's spring board competition at the 1996 olympics in atlanta.She somersaults from a 3-m bord. Her height, h metres, above the water t seconds after she leaves the springboard is given by h=-4.9tsquared+8.8t+3 what is the value of h when Palletier hits the water? what quadratic equation represents this situation?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Since the height of a dive is measured from the water, her height when she hits the water will be zero. So the equation at the moment she hits the water will be
0=-4.9t%5E2%2B8.8t%2B3
Since this does not factor we'll use the Quadratic Formula with "a" = -4.9, "b" = 8.8 and "c" = 3:
t+=+%28-%288.8%29+%2B-+sqrt%28%288.8%29%5E2+-+4%28-4.9%29%283%29%29%29%2F2%28-4.9%29
Simplifying we get:
t+=+%28-8.8+%2B-+sqrt%2877.44+-+4%28-4.9%29%283%29%29%29%2F2%28-4.9%29
t+=+%28-8.8+%2B-+sqrt%2877.44+%2B+58.8%29%29%2F%28-9.8%29
t+=+%28-8.8+%2B-+sqrt%28136.24%29%29%2F%28-9.8%29
t+=+%28-8.8+%2B-+11.6721891691318985%29%2F%28-9.8%29
Now we should split this into the two expressions for t:
t+=+%28-8.8+%2B+11.6721891691318985%29%2F%28-9.8%29 or t+=+%28-8.8+-+11.6721891691318985%29%2F%28-9.8%29
t+=+%282.8721891691318985%29%2F%28-9.8%29 or t+=+%28-20.4721891691318985%29%2F%28-9.8%29
Since the first answer is negative we will reject it. (It makes no sense to deal with any time before she started her dive!) Dividing out the second solution we get:
t = 2.0889988948093774
So she hits the water approximately 2 seconds after starting her dive.