SOLUTION: A ball is thrown upward from the roof of a building 100 m tall with an initial velocity of 20 m/s. Use this information for exercises 35 to 38. When will the ball reach a he

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A ball is thrown upward from the roof of a building 100 m tall with an initial velocity of 20 m/s. Use this information for exercises 35 to 38. When will the ball reach a he      Log On


   

Question 42743This question is from textbook
: A ball is thrown upward from the roof of a building 100 m tall with an initial velocity of 20 m/s. Use this information for exercises 35 to 38.


When will the ball reach a height of 80 m?
 This question is from textbook

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Use General Equation:
f%28x%29+=+-16t%5E2+%2B+vt+%2B+st%5E0 where v is the initial velocity and s is the height you started at
f%28x%29+=+-16t%5E2+%2B+20t+%2B+100
When will the ball reach a height of 80 m?
80+=+-16t%5E2+%2B+20t+%2B+100
0+=+-16t%5E2+%2B+20t+%2B+20
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -16t%5E2%2B20t%2B20+=+0) has the following solutons:

t%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=%2820%29%5E2-4%2A-16%2A20=1680.

Discriminant d=1680 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-20%2B-sqrt%28+1680+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2820%29%2Bsqrt%28+1680+%29%29%2F2%5C-16+=+-0.65586884574495
t%5B2%5D+=+%28-%2820%29-sqrt%28+1680+%29%29%2F2%5C-16+=+1.90586884574495

Quadratic expression -16t%5E2%2B20t%2B20 can be factored:
-16t%5E2%2B20t%2B20+=+-16%28t--0.65586884574495%29%2A%28t-1.90586884574495%29
Again, the answer is: -0.65586884574495, 1.90586884574495. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B20%2Ax%2B20+%29

About 1.9 seconds ....