SOLUTION: (This word problems involves using the quadratic formula) The height in feet of a ball thrown off the roof of a building is given by{{{h(t)=-16t^2+70t+75}}} , where t represents th

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: (This word problems involves using the quadratic formula) The height in feet of a ball thrown off the roof of a building is given by{{{h(t)=-16t^2+70t+75}}} , where t represents th      Log On


   

Question 304263: (This word problems involves using the quadratic formula) The height in feet of a ball thrown off the roof of a building is given byh%28t%29=-16t%5E2%2B70t%2B75 , where t represents the time in seconds since the ball was thrown. Determine to the nearest tenth of a second the time at which the ball strikes the ground at h=0. (steps will be appreciated)
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
h%28t%29=-16t%5E2%2B70t%2B75
.
Set h(t) to zero and solve for t:
0+=+-16t%5E2%2B70t%2B75
0+=+-16t%5E2%2B70t%2B75
Solve by applying the quadratic formula. Doing so will yield:
t = {-0.9, 5.3}
We can toss out the negative solution leaving:
t = 5.3 seconds
.
Details of quadratic formula to follow:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B70x%2B75+=+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=%2870%29%5E2-4%2A-16%2A75=9700.

Discriminant d=9700 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-70%2B-sqrt%28+9700+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2870%29%2Bsqrt%28+9700+%29%29%2F2%5C-16+=+-0.890268063061283
x%5B2%5D+=+%28-%2870%29-sqrt%28+9700+%29%29%2F2%5C-16+=+5.26526806306128

Quadratic expression -16x%5E2%2B70x%2B75 can be factored:
-16x%5E2%2B70x%2B75+=+-16%28x--0.890268063061283%29%2A%28x-5.26526806306128%29
Again, the answer is: -0.890268063061283, 5.26526806306128. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B70%2Ax%2B75+%29