SOLUTION: Please help me! Anne Pelletier won a bronze medal in the women's springboard competition at the 1996 Summer Olympics in Atlanta. Pelletier somersaults from a 3 m springboard. He

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me! Anne Pelletier won a bronze medal in the women's springboard competition at the 1996 Summer Olympics in Atlanta. Pelletier somersaults from a 3 m springboard. He      Log On


   

Question 237389: Please help me!
Anne Pelletier won a bronze medal in the women's springboard competition at the 1996 Summer Olympics in Atlanta. Pelletier somersaults from a 3 m springboard. Her height, h metres, above the water t seconds after she leaves the board is given by h=-4.9t%5E2%2B8.8t%2B3. How long is it until Pelletier reaches the water? How high is she after 0.5 seconds?

Thank you!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
somersaults from a 3 m springboard. Her height, h metres, above the water t seconds after she leaves the board is given by: h = -4.9t^2 + 8.8t + 3 .
How long is it until Pelletier reaches the water?
:
We she enters the water, h=0, therefore find t when h=0:
-4.9t^2 + 8.8t + 3 = 0
Use the quadratic formula to find the positive solution here:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem x=t; a=-4.9; b=8.8; c=3
t+=+%28-8.8+%2B-+sqrt%288.8%5E2+-+4+%2A-4.9%2A3+%29%29%2F%282%2A-4.9%29+
:
t+=+%28-8.8+%2B-+sqrt%2877.44+-+%28-58.8%29+%29%29%2F%28-9.8%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+
:
We want the positive solution only
t+=+%28-8.8+-+11.67%29%2F%28-9.8%29+
t = %28-20.47%29%2F%28-9.8%29
t = +2.1 sec to strike the water
:
How high is she after 0.5 seconds?
h = -4.9(.5^2) + 8.8(.5) + 3
:
h = -4.9(.25) + 4.4 + 3
:
h = -1.225 + 4.4 + 3
:
h = 6.175 meters high in .5 seconds