SOLUTION: Please help with this problem, this is what I have so far: Problem: Height of a projected ball, An astronaut on the moon throws a baseball upward. The astronaut is 6ft., 6in.

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Question 268286: Please help with this problem, this is what I have so far:
Problem: Height of a projected ball,
An astronaut on the moon throws a baseball upward. The astronaut is 6ft., 6in. tall, and the initial velocity of the ball is 30 ft. per sec. The height S of the ball in feet is given by the equation
S= -2.7t^2 + 30t + 6.5
where t is the number of seconds after the ball was thrown.
A.) After how many seconds is the ball 12ft above the moon's surface? Round to the nearest hundreth.
I know I have to look for the seconds, which is t so then I have to solve for S, the height. This is have I've got so far:
12 = 2.7t^2 + 30t + 6.5
-12 -12
------------------------
0 = 2.7t^2 + 30t - 5.5

B.)How many seconds will it take fore the ball to return to the surface? Round to the nearest hundredth.
So on the second part of the equation I have to look for the time, so that means that I have to solve for the height...

Thanks for your help in advance.
Found 2 solutions by Alan3354, scott8148:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
An astronaut on the moon throws a baseball upward. The astronaut is 6ft., 6in. tall, and the initial velocity of the ball is 30 ft. per sec. The height S of the ball in feet is given by the equation
S= -2.7t^2 + 30t + 6.5
where t is the number of seconds after the ball was thrown.
A.) After how many seconds is the ball 12ft above the moon's surface? Round to the nearest hundreth.
I know I have to look for the seconds, which is t so then I have to solve for S, the height. This is have I've got so far:
12 = 2.7t^2 + 30t + 6.5 *** It's -2.7
-12 -12
------------------------
0 = -2.7t^2 + 30t - 5.5
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2.7x%5E2%2B30x%2B-5.5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2830%29%5E2-4%2A-2.7%2A-5.5=840.6.

Discriminant d=840.6 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-30%2B-sqrt%28+840.6+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2830%29%2Bsqrt%28+840.6+%29%29%2F2%5C-2.7+=+0.18646247628908
x%5B2%5D+=+%28-%2830%29-sqrt%28+840.6+%29%29%2F2%5C-2.7+=+10.924648634822

Quadratic expression -2.7x%5E2%2B30x%2B-5.5 can be factored:
-2.7x%5E2%2B30x%2B-5.5+=+%28x-0.18646247628908%29%2A%28x-10.924648634822%29
Again, the answer is: 0.18646247628908, 10.924648634822. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2.7%2Ax%5E2%2B30%2Ax%2B-5.5+%29

---------------
Notice there are 2 numbers, the smallest is going up, the other coming back down.
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B.)How many seconds will it take for the ball to return to the surface? Round to the nearest hundredth.
It's at the surface when h = 0
-2.7t^2 + 30t + 6.5 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2.7x%5E2%2B30x%2B6.5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2830%29%5E2-4%2A-2.7%2A6.5=970.2.

Discriminant d=970.2 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-30%2B-sqrt%28+970.2+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2830%29%2Bsqrt%28+970.2+%29%29%2F2%5C-2.7+=+-0.212598823296627
x%5B2%5D+=+%28-%2830%29-sqrt%28+970.2+%29%29%2F2%5C-2.7+=+11.3237099344077

Quadratic expression -2.7x%5E2%2B30x%2B6.5 can be factored:
-2.7x%5E2%2B30x%2B6.5+=+%28x--0.212598823296627%29%2A%28x-11.3237099344077%29
Again, the answer is: -0.212598823296627, 11.3237099344077. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2.7%2Ax%5E2%2B30%2Ax%2B6.5+%29

------------
Ignore the negative number.
t = 11.32 seconds
So on the second part of the equation I have to look for the time, so that means that I have to solve for the height...

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
A.) just use the quadratic formula on the equation you generated and solve for t
___ watch the signs (your equation has an incorrect sign for the coefficient of the squared term)

B.) substitute zero for S in the original equation (S= -2.7t^2 + 30t + 6.5) and use the quadratic formula

check the solutions for t to see if they make sense
___ A should have two solutions (upward and downward)
___ B should have one solution (negative value not realistic)