# Mechanics problem

### Mechanics problem

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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Joined: Mon Apr 09, 2007 3:58 pm
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For a free falling object, the distance D covered in a given time interval (t, T) can be expressed as:

$$D = \frac{1}{ 2}g(T^2 - t^2)$$

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

$$60 = \frac{1}{2}g(T^2 - t^2)$$ ......................(1)
$$T - t = 2$$ .....................................................(2)

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

$$H = \frac{1}{2}gT^2 = \frac{1}{2}g4^2 = 80$$

So
It take the body 4 seconds to fall 80 meters

redmafiya

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Location: New Zealand
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