# An earthquake causes a 3 kg book to fall from a shelf. If the book lands with a speed of 4 m/s, from what height did it fall?

This can be solved using either kinematics or energy conservation, both methods assuming no outside forces.

Energy Conservation

Kinematics

Because the book begins from rest:

We plug in our values:

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Using the equation of motion for free fall, ( v^2 = u^2 + 2gh ), where ( v ) is the final velocity (4 m/s), ( u ) is the initial velocity (0 m/s, as the book starts from rest), ( g ) is the acceleration due to gravity (9.8 m/s²), and ( h ) is the height.

Rearranging the equation to solve for ( h ): [ h = \frac{{v^2 - u^2}}{{2g}} ]

Plugging in the given values: [ h = \frac{{(4 , \text{m/s})^2 - (0 , \text{m/s})^2}}{{2 \times 9.8 , \text{m/s}^2}} ]

[ h = \frac{{16 , \text{m}^2/\text{s}^2}}{{19.6 , \text{m/s}^2}} ]

[ h = 0.816 , \text{m} ]

So, the book fell from a height of approximately 0.816 meters.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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