21st Century Astronomy (sixth Edition)
6th Edition
ISBN: 9780393675504
Author: Laura Kay, Stacy Palen, George Blumenthal
Publisher: W. W. Norton & Company
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Chapter 1, Problem 27QP
To determine
Whether the horoscope sign consistently best describe your experiences.
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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
An outfielder throws a baseball to his catcher in an attempt to throw out a runner at home plate. The ball bounces once before reaching the catcher. Assume the angle at which the bounced ball leaves the ground is the same as the angle at which the outfielder threw it as shown in the figure, but that the ball's speed after the bounce is one-half of what it was before the bounce.
8
(a) Assuming the ball is always thrown with the same initial speed, at what angle & should the fielder throw the ball to make it go the same distance D with one bounce (blue path) as a ball thrown upward at 35.0° with no bounce (green path)?
24
(b) Determine the ratio of the time interval for the one-bounce throw to the flight time for the no-bounce throw.
Cone-bounce
no-bounce
0.940
Chapter 1 Solutions
21st Century Astronomy (sixth Edition)
Ch. 1.1 - Prob. 1.1CYUCh. 1.2 - Prob. 1.2CYUCh. 1.3 - Prob. 1.3CYUCh. 1 - Prob. 1QPCh. 1 - Prob. 2QPCh. 1 - Prob. 3QPCh. 1 - Prob. 4QPCh. 1 - Prob. 5QPCh. 1 - Prob. 6QPCh. 1 - Prob. 7QP
Ch. 1 - Prob. 8QPCh. 1 - Prob. 9QPCh. 1 - Prob. 10QPCh. 1 - Prob. 11QPCh. 1 - Prob. 12QPCh. 1 - Prob. 13QPCh. 1 - Prob. 14QPCh. 1 - Prob. 15QPCh. 1 - Prob. 16QPCh. 1 - Prob. 17QPCh. 1 - Prob. 18QPCh. 1 - Prob. 19QPCh. 1 - Prob. 20QPCh. 1 - Prob. 21QPCh. 1 - Prob. 22QPCh. 1 - Prob. 23QPCh. 1 - Prob. 24QPCh. 1 - Prob. 25QPCh. 1 - Prob. 26QPCh. 1 - Prob. 27QPCh. 1 - Prob. 28QPCh. 1 - Prob. 29QPCh. 1 - Prob. 30QPCh. 1 - Prob. 31QPCh. 1 - Prob. 32QPCh. 1 - Prob. 33QPCh. 1 - Prob. 34QPCh. 1 - Prob. 35QPCh. 1 - Prob. 36QPCh. 1 - Prob. 37QPCh. 1 - Prob. 38QPCh. 1 - Prob. 39QPCh. 1 - Prob. 40QPCh. 1 - Prob. 41QPCh. 1 - Prob. 42QPCh. 1 - Prob. 43QPCh. 1 - Prob. 44QPCh. 1 - Prob. 45QP
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