SOLUTION: A ball is thrown from a height of 141 feet with an initial downward velocity of 21 ft/s. The balls height “h” (in feet) after “t” seconds is given by the following. H=141

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A ball is thrown from a height of 141 feet with an initial downward velocity of 21 ft/s. The balls height “h” (in feet) after “t” seconds is given by the following. H=141      Log On


   

Question 1145786: A ball is thrown from a height of 141 feet with an initial downward velocity of 21 ft/s. The balls height “h” (in feet) after “t” seconds is given by the following.
H=141-21t-16t squared
How long after the ball is thrown does it hit the ground?
Round to the nearest hundredth
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
H=141-21t-16t squared
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Impact is at h = 0
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h = 141 - 21t - 16t^2 = 0
-16t^2 - 21t + 141 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B-21x%2B141+=+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=%28-21%29%5E2-4%2A-16%2A141=9465.

Discriminant d=9465 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--21%2B-sqrt%28+9465+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-21%29%2Bsqrt%28+9465+%29%29%2F2%5C-16+=+-3.69650723623841
x%5B2%5D+=+%28-%28-21%29-sqrt%28+9465+%29%29%2F2%5C-16+=+2.38400723623841

Quadratic expression -16x%5E2%2B-21x%2B141 can be factored:
-16x%5E2%2B-21x%2B141+=+%28x--3.69650723623841%29%2A%28x-2.38400723623841%29
Again, the answer is: -3.69650723623841, 2.38400723623841. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B-21%2Ax%2B141+%29


Ignore the negative solution.