Cosmic Perspective Fundamentals
Cosmic Perspective Fundamentals
3rd Edition
ISBN: 9780134988504
Author: Bennett, Jeffrey O., Donahue, M. (megan), SCHNEIDER, Nicholas, Voit, Mark
Publisher: Pearson,
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Chapter 12, Problem 20SEQ

Explain all answers clearly, with complete sentences and proper essay structure if needed. An asterisk (*) designates a quantitative problem, for which you should show all your work.

Distances Between Galaxies. If you were to divide the present-day universe up into cubes with sides 10 million light-years long, each cube would contain, on average, about one galaxy similar in size to the Milky Way. Now suppose you traveled back in time, to an era when the average distance between galaxies was one-quarter of its current value. How many galaxies similar in size to the Milky Way would you expect to find, on average, in cubes of the same size? In order to simplify the problem, assume that the total number of galaxies of each type has not changed between then and now. Based on your answer, would you expect collision, to be much more frequent at that time or only moderately more frequent?

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Figure 8.14 shows a cube at rest and a small object heading toward it. (a) Describe the directions (angle 1) at which the small object can emerge after colliding elastically with the cube. How does 1 depend on b, the so-called impact parameter? Ignore any effects that might be due to rotation after the collision, and assume that the cube is much more massive than the small object. (b) Answer the same questions if the small object instead collides with a massive sphere.
2. A projectile is shot from a launcher at an angle 0,, with an initial velocity magnitude vo, from a point even with a tabletop. The projectile hits an apple atop a child's noggin (see Figure 1). The apple is a height y above the tabletop, and a horizontal distance x from the launcher. Set this up as a formal problem, and solve for x. That is, determine an expression for x in terms of only v₁, 0, y and g. Actually, this is quite a long expression. So, if you want, you can determine an expression for x in terms of v., 0., and time t, and determine another expression for timet (in terms of v., 0.,y and g) that you will solve and then substitute the value of t into the expression for x. Your final equation(s) will be called Equation 3 (and Equation 4).
Draw a phase portrait for an oscillating, damped spring.
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