Question 237389
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 = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In this problem x=t; a=-4.9; b=8.8; c=3
{{{t = (-8.8 +- sqrt(8.8^2 - 4 *-4.9*3 ))/(2*-4.9) }}}
:
{{{t = (-8.8 +- sqrt(77.44 - (-58.8) ))/(-9.8) }}}
:
{{{t = (-8.8 +- sqrt(77.44 + 58.8 ))/(-9.8) }}}
:
{{{t = (-8.8 +- sqrt(136.24 ))/(-9.8) }}}
:
We want the positive solution only
{{{t = (-8.8 - 11.67)/(-9.8) }}}
t = {{{(-20.47)/(-9.8)}}}
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