SOLUTION: Can you please help me solve this story problem. A ball is thrown downward from a window in a tall building. It's position at time t in seconds is s=16t^2+32t, where s is in feet.

Question 476328: Can you please help me solve this story problem. A ball is thrown downward from a window in a tall building. It's position at time t in seconds is s=16t^2+32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 217 feet?
Found 2 solutions by jorel1380, stanbon:
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
16t2+32t=217
16t2+32t-217=0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=14912 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.81608438061844, -4.81608438061844. Here's your graph:

The two answers are 2.81608438061844, -4.8160843806184. Throwing out the negative answer, we get t=2.816..
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A ball is thrown downward from a window in a tall building. It's position at time t in seconds is s=16t^2+32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 217 feet?
---
Solve:
16t^2+32t = 217
----
t = [-32 +- sqrt(32^2-4*16*-217)]/(2*32)
------
t = [-32 +- 122.11]/64
---
Positive solution:
t = 1.41 seconds
==================
Cheers,
Stan H.
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