Chapter 4: Problem 15
Which is thought to be more prevalent in the universe, dark matter or dark energy?
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
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Chapter 4: Problem 15
Which is thought to be more prevalent in the universe, dark matter or dark energy?
These are the key concepts you need to understand to accurately answer the question.
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Consider a space pod somewhere between Earth and the Moon, at just the right distance so that gravitational attraction to Earth and gravitational attraction to the Moon are equal. Is this location nearer Earth or nearer the Moon?
Two golfers each hit a ball at the same speed, but one hits it at \(60^{\circ}\) with the horizontal and the other at \(30^{\circ}\). Which ball goes farther? Which hits the ground first? (Ignore air resistance.)
(Here's a Chapter 4-type question): The first stage of each SpaceX rocket that services the ISS no longer is dumped into the sea, but is returned for recycling (when all goes well). As the empty first stage falls back to Earth, one of its main engines slows its descent velocity to zero at the moment of touchdown. Is it correct to say that during this maneuver, the velocity and the acceleration of the first stage are in opposite directions? Defend your answer.
A baseball is tossed at a steep angle into the air and makes a smooth parabolic path. Its time in the air is t, and it reaches a maximum height \(b .\) Assume that air resistance is negligible. (a) Show that the height reached by the ball is \(\frac{g t^{2}}{8}\). (b) Show that if the ball is in the air for \(4 \mathrm{~s}\), it reaches a height of nearly \(20 \mathrm{~m}\). (c) If the ball reached the same height as it did when it was tossed at some other angle, would the time of flight be the same?
An airplane is flying horizontally with speed \(1000 \mathrm{~km} / \mathrm{h}\) \((280 \mathrm{~m} / \mathrm{s})\) when an engine falls off. Neglecting air resistance, assume that it takes \(30 \mathrm{~s}\) for the engine to hit the ground. (a) Show that the altitude of the airplane is \(4.4 \mathrm{~km}\). (Use \(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\).) (b) Show that the horizontal distance that the airplane engine travels during its fall is \(8.4 \mathrm{~km}\). (c) If the airplane somehow continues to fly as though nothing had happened, where is the engine relative to the airplane at the moment the engine hits the ground?
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