SOLUTION: How long does it take a ball to reach the ground 7.0 m below, if it is thrown straight up with an initial speed of 2.0 m/s?

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Question 892682: How long does it take a ball to reach the ground 7.0 m below, if it is thrown straight up with an initial speed of 2.0 m/s?
Found 2 solutions by Alan3354, Fombitz:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How long does it take a ball to reach the ground 7.0 m below, if it is thrown straight up with an initial speed of 2.0 m/s?
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9.8 m/sec/sec is commonly used for gravity's acceleration on Earth.
Height as a function of time is:
h(t) = -4.9t^2 + 2t + 7 h in meters, t in seconds
h(t) = 0 at impact
-4.9t^2 + 2t + 7 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4.9x%5E2%2B2x%2B7+=+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=%282%29%5E2-4%2A-4.9%2A7=141.2.

Discriminant d=141.2 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+141.2+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+141.2+%29%29%2F2%5C-4.9+=+-1.00844496142963
x%5B2%5D+=+%28-%282%29-sqrt%28+141.2+%29%29%2F2%5C-4.9+=+1.41660822673575

Quadratic expression -4.9x%5E2%2B2x%2B7 can be factored:
-4.9x%5E2%2B2x%2B7+=+%28x--1.00844496142963%29%2A%28x-1.41660822673575%29
Again, the answer is: -1.00844496142963, 1.41660822673575. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B2%2Ax%2B7+%29

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Ignore the negative value
t =~ 1.4166 seconds

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
s=-%281%2F2%29gt%5E2%2Bv0%2At%2Bs0
s=-%281%2F2%29%289.8%29t%5E2%2B2t%2B7
s=-4.9t%5E2%2B2t%2B7
Find t when,
s=0
.
.
.
-4.9t%5E2%2B2t%2B7=0
Use the quadratic formula,
t=%28-2+%2B-+sqrt%282%5E2-4%28-4.9%29%287%29%29%29%2F%282%28-4.9%29%29
t=%28-2%2B-sqrt%28141.2%29%29%2F%28-9.8%29
Only the positive time makes sense here.
t=%28-2-11.883%29%2F%28-9.8%29
t=1.41sec