SOLUTION: Using a powerful air gun, a steel ball is shot vertically upward with a velocity of 80 meters per second, followed by another shot after 5 sec. Find the initial velocity of the sec

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Question 950010: Using a powerful air gun, a steel ball is shot vertically upward with a velocity of 80 meters per second, followed by another shot after 5 sec. Find the initial velocity of the second ball in order to meet the first ball 150 meters from the ground.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Using a powerful air gun, a steel ball is shot vertically upward with a velocity of 80 meters per second, followed by another shot after 5 sec. Find the initial velocity of the second ball in order to meet the first ball 150 meters from the ground.
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Using 5 m/sec/sec as gravity influence:
For the 1st ball:
h(t) = -5t^2 + 80t
For h(t) = 150
-5t^2 + 80t = 150
t^2 - 16t + 30 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-16x%2B30+=+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=%28-16%29%5E2-4%2A1%2A30=136.

Discriminant d=136 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+136+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+136+%29%29%2F2%5C1+=+13.8309518948453
x%5B2%5D+=+%28-%28-16%29-sqrt%28+136+%29%29%2F2%5C1+=+2.1690481051547

Quadratic expression 1x%5E2%2B-16x%2B30 can be factored:
1x%5E2%2B-16x%2B30+=+%28x-13.8309518948453%29%2A%28x-2.1690481051547%29
Again, the answer is: 13.8309518948453, 2.1690481051547. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-16%2Ax%2B30+%29

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t = 2.169 seconds ascending, less than 5 seconds --> not possible for them to meet.
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t = 13.831 seconds descending at 150 meters.
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The 2nd ball has to get to 150 meters in 8.831 seconds (13.831 - 5)
h(t) = -5t^2 + v*t
150 = -5*8.831^2 + v*8.831
8.831v = 539.9328
v =~ 61.1406 m/sec