Mechanics problem

Mechanics problem

Postby kate » Mon Jun 30, 2008 1:18 pm

A body is falling freely without a beginning speed from height H and the last h = 60 m passes for time t<sub>1</sub> = 2 s.
a) What is the time of falling of the ball?
b) How many meters is the height H?
kate
 
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Postby redmafiya » Fri Jul 11, 2008 11:39 pm

For a free falling object, the distance D covered in a given time interval (t, T) can be expressed as:

[tex]D = \frac{1}{ 2}g(T^2 - t^2)[/tex]

So we can set up a system of two equations based on the given information:

[tex]60 = \frac{1}{2}g(T^2 - t^2)[/tex] ......................(1)
[tex]T - t = 2[/tex] .....................................................(2)

Solving for T and t, we have
[tex]T = 1 +\frac{30}{g} = 4[/tex]
[tex]t = T - 2 = 2[/tex]

[tex]H = \frac{1}{2}gT^2 = \frac{1}{2}g4^2 = 80[/tex]

So
It take the body 4 seconds to fall 80 meters

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