Question 49724
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A ball is thrown upward from the roof of a 
building 100m tall with an initial 
velocity of 20m/s when will the ball reach 
a height of 80m

The formula is

s = s<sub>O</sub> + v<sub>O</sub>t + atē/2

where
s = h = the height of the ball off the ground in meters
s<sub>O</sub> = h<sub>O</sub> = the initial height = 100 m
v<sub>O</sub> = the initial velocity = 20 m/s
t = the number of seconds
a = g = -9.8 m/sē (the acceleration of gravity)

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Substituting:

h = (100) + (20)t + (-9.8)tē/2

h = 100 + 20t - 4.9tē

That's the formula for the height h in meters 
at any time t seconds.

Plug in h = 80m and solve for t

80 = 100 + 20t - 4.9tē 

4.9tē - 20t - 20 = 0

If you like, clear of decimals by multiplying 
thru by 10

49tē - 200t - 200 = 0

Use the quadratic formula and you'll get

t = -.83 and 4.92, approximately

Discard the negative answer.  The legitimate answer is
4.92 seconds.

Analysis:

at 0 seconds, the height is 100 m
at 1 second, the height is 115.1 m
at 2 seconds the height is 120.4 m

then it starts falling

at 3 seconds, its height is 115.9 m
at 4 seconds its height is 101.6 m
at 4.92 seconds its height is 80m
at 5 seconds its height is 77.5 m
at 6 seconds its height is 43.6 m
at 7 seconds its height is 0, i.e., it hits the ground.

Edwin</pre></font></b>