SOLUTION: A ball is thrown vertically upward from the Leaning Tower of Pisa (176 feet high)with an initial velocity of 96 feet per second. The height of the ball is described by the formula

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Question 221721: A ball is thrown vertically upward from the Leaning Tower of Pisa (176 feet high)with an initial velocity of 96 feet per second. The height of the ball is described by the formula -16t^2 + 96t +176. How long will it take the ball to hit the ground?
Please help I have tried to solve this several different ways and none of them are coming out to anything that makes sense. The example in the textbook shows it starting to be solved by factoring out -16 , but I can't see were it can go from there?
Answer by rapaljer(4671) (Show Source):
You can put this solution on YOUR website!
When the ball hits the ground, h=0, so set the equation equal to zero.
-16t^2 + 96t +176=0
-16(t^2 - 6t - 11)=0

What results here is a quadratic equation that cannot be factored. You will have to use the quadratic formula or completing the square. It turns out that completing the square is easier for this problem.

t^2 -6t -11=0
t^2 -6t +_____= 11+_____
Take HALF of the coefficient of t, which is -6 and SQUARE it. Half of -6 would be -3, and -3 squared is +9. Add =9 to each side:
t^2 -6t+9 = 11+9
(t-3)^2 = 20

Now you can take square root of each side like this:

Then add +3 to each side:

Reject the negative value since time cannot be negative.

Finally, either calculate this, or simplify the square root. By approximation (my calculator is in the other room!) square root of 20 is about 4.5, so the time is about 3+4.5= 7.5 seconds--very approximately!!

The exact value is this:

R^2

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamone Springs Campus