COLLEGE PHYSICS
COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 28, Problem 42QAP
To determine

(a)

How many dark matter particles are there in one cubic meter, if the average density of dark matter in our Milky Way galaxy is thought to be about 5 x 1023kg/m3.

To determine

(b)

There are about 2.7 x 1025 molecules per cubic meter in the air around you and a total of about 1019 grains of sands on all the beaches on earth. Relatively speaking, which is more likely: finding a dark matter particle in the air around you, or finding one particular grain of sand somewhere on one of Earth's beaches?

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A ball is thrown with an initial speed v, at an angle 6, with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/4. In terms of R and g, find the following. (a) the time interval during which the ball is in motion 2R (b) the ball's speed at the peak of its path v= Rg 2 √ sin 26, V 3 (c) the initial vertical component of its velocity Rg sin ei sin 20 (d) its initial speed Rg √ sin 20 × (e) the angle 6, expressed in terms of arctan of a fraction. 1 (f) Suppose the ball is thrown at the same initial speed found in (d) but at the angle appropriate for reaching the greatest height that it can. Find this height. hmax R2 (g) Suppose the ball is thrown at the same initial speed but at the angle for greatest possible range. Find this maximum horizontal range. Xmax R√3 2
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