SOLUTION: A ball is thrown upward from the roof a building 100 m tall with an initial velocity of 20 m/s - when will the ball reach a height of 80 m? 80 = -16t^2 + 20t + 100 16t^2 -20t -

Question 90368This question is from textbook Beginning Algebra
: A ball is thrown upward from the roof a building 100 m tall with an initial velocity of 20 m/s - when will the ball reach a height of 80 m?
80 = -16t^2 + 20t + 100
16t^2 -20t -20 = 0
4t^2 - 5t - 5 = 0
t = -(-5) +/- radical (-5)^2 - 4(4)(-5) over 2(4)
t = 5 +/- radical 25 + 80 over 8
t = 5 + 10.247 over 8
t = 15.247 over 8
t = 1.906 seconds
Please confirm if I'm doing this correctly - thank you. This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Subtract 80 from both sides

Subtract 80 from both sides

Let's use the quadratic formula to solve for t:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-16, b=20, and c=20

Square 20 to get 400

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and -16 to get -32

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

Since a negative time doesn't make sense, our only solution is:

So you are correct
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