SOLUTION: A ball is thrown upward from the roof of a building 100 m tall with an initial velocity of 20m/s. 36. When will the ball reach a height of 80m? Above is part o

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Question 46367This question is from textbook beginning algebra
: A ball is thrown upward from the roof of a building 100 m tall with an
initial velocity of 20m/s.
36. When will the ball reach a height of 80m?
Above is part of the problem.
I am totally confused with this problem.
This question is from textbook beginning algebra

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You first need to know the formula for the height of an object thrown upwards as a function of time.
h%28t%29+=+-4.9t%5E2%2BVot%2BHo Where:
h(t) is the height as a function of time, t, in seconds.
Vo is the initial upward velocity in meters per second.
Ho is the initial height from which the object is thrown, in meters.
For your problem, Vo = 20 m/s
Ho = 100 meters.
h(t) = 80 meters.
Plug these values into the formula and solve for t, the time.
80+=+-4.9t%5E2%2B20t%2B100 Subtract 80 from both sides of the equation.
-4.9t%5E2%2B20t%2B20+=+0 Use the quadratic formula to solve:t=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
In this problem, a=-4.9, b=20, and c=20
t+=+%28-20%2B-sqrt%2820%5E2-4%28-4.9%29%2820%29%29%29%2F2%28-4.9%29
t+=+%28-20%2B-sqrt%28400%2B392%29%29%2F-9.8
t+=+%28-20%2B-sqrt%28792%29%29%2F-9.8
t+=+2.04%2B%28-2.87%29 or t+=+2.04-%28-2.87%29
t+=+-0.83 or t+=+4.91 Discard the negative solution as the time must be a positive value.
The answer is: The ball will reach a height of 80 meters in t = 4.91 seconds.