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A baseball dropped from the roof of a tall building takes 5.23 second s to reach the ground. How tall is the building?

User Scolestock
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1 Answer

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The most general formula useful here would be

s = s0 + v0*t + (1/2)at^2, where s0 is the original height, v0 is the original velocity, a is the acceleration, and t is the time.

Here, s becomes 0 (baseball is on the ground)
v0 is 0, since the initial speed of the ball was 0.
a is the acc'n due to gravity, and is -9.8 m per (sec)^2 in the metric sys.
t is known and is 5.23 sec

All that is left to find is s0, the original height (which is the building height).

0 = s0 + (0)(5.23 sec) + (1/2) (-9.8 m per sec^2)(5.23 sec)^2

-s0 = 0 - (4.9 m per sec^2) ( 27.35 sec^2)

So s0 = 134 meters (approx)

The building height was approx. 134 meters.
User Justkris
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