SOLUTION: Jacqueline threw a ball from 1 m above the ground. The ball reached a maximum height of 46 m at 3 seconds. a) Determine the equation that will model the parabola for this situa

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Question 1090546: Jacqueline threw a ball from 1 m above the ground. The ball reached a maximum height of 46 m at 3 seconds.
a) Determine the equation that will model the parabola for this situation.
b) How long does it take until the ball hits the ground
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jacqueline threw a ball from 1 m above the ground.
The ball reached a maximum height of 46 m at 3 seconds.
:
a) Determine the equation that will model the parabola for this situation.
Using the equation where f(t) = the height in t seconds at a v velocity m/sec
f(t) = -4.9t^2 + vt + 1
replace f(t) with 46 and t with 3 sec, find the initial velocity (v)
-4.9(3^2) + 3v + 1 = 46
-4.9(9) + 3v = 46 - 1
-44.1 + 3v = 45
3v = 45 + 44.1
v = 89.1/3
v = 29.7 m/sec is the initial upward velocity
The equation: f(t) = -4.9t^2 + 29.7t + 1
Looks like this
+graph%28+300%2C+200%2C+-4%2C+10%2C+-10%2C+55%2C+-4.9x%5E2%2B29.7x%2B1%29+

b) How long does it take until the ball hits the ground
then f(t) = 0
-4.9t^2 + 29.1t + 1 = 0
Use the quadratic formula; a=-4.9; b=29.7; c=1
I got a positive solution of
t = 6.0947 sec to his the ground