Because of your physics background, you have been hired as a consultant for a ne

Question

Because of your physics background, you have been hired as a consultant for a new movie about Galileo. In one scene, he climbs up to the top of a tower and, in frustration over the people who ridicule his theories, throws a rock at a group of them standing on the ground. The rock leaves his hand at 30º above the horizontal. The script calls for the rock to land 16.65 m from the base of the tower near a group of his detractors. It is important for the script that the rock take precisely 3.0 seconds to hit the ground so that there is time for a good expressive close-up. The set coordinator is concerned that the rock will hit the ground with too much speed causing cement chips from the plaza to injure one of the high priced actors. What is the speed at which the rock should be thrown?

Explanation / Answer

the horizontal component of the velocity does not change since no force acts on it we can use distance equals rate times time d = rt r = d/t = 16.65/3.0 = 5.55m/s this is the horizontal component of the velocity. V tot cos(30) = this horizontal component Most of the throw is horizontal since the angle is closer to horizontal (0 deg) than it is to vertical (90 deg). cos(30) > sin(30), so we use cos(30) for the horizontal component. V tot cos(30) = 5.55m/s Vtot = (5.55m/s)/cos(30) V tot = 6.41 m/s The rock should be thrown at 6.41 m/s

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