Question 99132: Find the time required for an object to fall to the ground from a building that is 1400 ft high Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! The equation you are looking for is:
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in which the letters represent the following:
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h = the height above ground at the time t (in feet)
t = the elapsed time after the object is released (in seconds)
vo = the initial vertical velocity in feet per second that the object has at release
ho = the initial height above ground when the object is released
a = the acceleration in feet per second^2 due to gravity (usually 32 ft/sec^2 is acceptable)
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The initial vertical velocity (vo) of the object is zero because the object is not thrown
upward or downward. It is just released. Therefore, the term is zero and
can be deleted from the equation.
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The initial height of the object is 1400 feet because that is the height above
ground of the object when it is released.
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After an unknown number of seconds passes, the object hits the ground and at that time
its height above ground is zero. Therefore, we can set h equal to zero.
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With these substitutions into the equation (including that a = 32) the equation becomes:
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Multiply the to get -16. Substitute this into the equation and it becomes:
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Get rid of the 1400 on the right side by subtracting 1400 from both sides to make the
equation become:
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Divide both sides of this equation by -16, the multiplier of the and the equation
reduces to:
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Solve for t by taking the square root of both sides:
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Calculator time ... the square root of 87.5 seconds^2 is 9.354143467 seconds
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So the answer to this problem is about 9.4 seconds
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No sense in having too much accuracy. The acceleration due to gravity on Earth is probably
closer to 32.2 feet per second^2 and it varies depending upon where you are on the globe.
But for most physics problems 32 feet per second^2 is close enough.
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Hope this helps you to understand the problem. If you get into calculus a little (1st
semester probably) you'll find out where the equation that we used comes from.
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