A person on the street wants to throw an 8 kg book up to a person leaning out of a window 5 m above street level. With what velocity must the person throw the book so that it reaches the person in the window?

5 m/s

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8 m/s

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10 m/s

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40 m/s

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Solution

The correct option is C 10 m/s
When the book reaches the person in the window, it will have a gravitational potential energy of U = mgh. In order for the book to reach the window, then, it must leave the hands of the person at street level with at least that much kinetic energy. Kinetic energy is given by the formula $K E = \frac{1}{2} m v^{2}$ , so we can solve for v by making KE = U:
$\frac{1}{2} m v^{2} = m g h v = \sqrt{2 (10 m / s^{2}) (5 m)}$
$v^{2} = 2 g h = \sqrt{100 m^{2} / S^{2}}$
$= 10 m / s$

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