COLLEGE PHYSICS (LL W/WEBASSIGN)
11th Edition
ISBN: 9781337741644
Author: SERWAY
Publisher: CENGAGE L
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Chapter 3, Problem 56AP
Antlion larvae lie in wait for prey at the bottom of a conical pit about 5.0 cm deep and 3.8 cm in radius. When a small insect ventures into the pit, it slides to the bottom and is seized by the antlion. If the prey attempts to escape, the antlion rapidly launches grains of sand at the prey, either knocking it down or causing a small avalanche that returns the prey to the bottom of the pit. Suppose an antlion launches grains of sand at an angle of 72° above the horizon. Find the launch speed v0 required to hit a target at the top of the pit, 5.0 cm above and 3.8 cm to the right of the antlion.
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Question 03
i)
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Question 04
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Chapter 3 Solutions
COLLEGE PHYSICS (LL W/WEBASSIGN)
Ch. 3.1 - Which of the following objects cant be...Ch. 3.1 - Consider the following controls in an automobile:...Ch. 3.1 - A girl on a bicycle takes 15.0 s to ride half way...Ch. 3.1 - Suppose you are carrying a ball and running at...Ch. 3.1 - As a projectile moves in its parabolic path, where...Ch. 3 - As a projectile moves in its path, is there any...Ch. 3 - Construct motion diagrams showing the velocity and...Ch. 3 - Explain whether the following particles do or do...Ch. 3 - A ball is projected horizontally from the top of a...Ch. 3 - A projectile is launched with speed v0 at an angle...
Ch. 3 - Determine which of the following moving objects...Ch. 3 - Two projectiles are thrown with the same initial...Ch. 3 - A ball is thrown upward in the air by a passenger...Ch. 3 - A projectile is launched at some angle to the...Ch. 3 - A baseball is thrown from the outfield toward the...Ch. 3 - A student throws a heavy red ball horizontally...Ch. 3 - A boat is heading due east at speed v when...Ch. 3 - As an apple tree is transported by a truck moving...Ch. 3 - An airplane in a holding pattern flies at constant...Ch. 3 - A hiker walks 2.00 km north and then 3.00 km east,...Ch. 3 - A miniature quadcopter is located at xi = 2.00 m...Ch. 3 - An ant crawls on the floor along the curved path...Ch. 3 - Explain whether the following particles do or do...Ch. 3 - A rabbit is moving in the positive x-direction at...Ch. 3 - A student stands at the edge of a cliff and throws...Ch. 3 - One of the fastest recorded pitches in major...Ch. 3 - The best leaper in the animal kingdom is the puma,...Ch. 3 - A rock is thrown upward from the level ground in...Ch. 3 - A placekicker must kick a football from a point...Ch. 3 - The record distance in the sport of throwing...Ch. 3 - A brick is thrown upward from the top of a...Ch. 3 - From the window of a building, a ball is tossed...Ch. 3 - A car is parked on a cliff overlooking the ocean...Ch. 3 - An artillery shell is fired with an initial...Ch. 3 - A projectile is launched with an initial speed of...Ch. 3 - A fireman d = 50.0 m away from a burning building...Ch. 3 - A playground is on the flat roof of a city school,...Ch. 3 - A cruise ship sails due north at 4.50 m/s while a...Ch. 3 - Suppose a boat moves at 12.0 m/s relative to the...Ch. 3 - A car travels due east with a speed of 50.0 km/h....Ch. 3 - A jet airliner moving initially at 3.00 102 mi/h...Ch. 3 - A Coast Guard cutter detects an unidentified ship...Ch. 3 - A bolt drops from the ceiling of a moving train...Ch. 3 - An airplane maintains a speed of 630 km/h relative...Ch. 3 - Suppose a chinook salmon needs to jump a waterfall...Ch. 3 - An airplane maintains a speed of 630 km/h relative...Ch. 3 - A river has a steady speed of 0.500 m/s. A student...Ch. 3 - This is a symbolic version of Problem 29. A river...Ch. 3 - How long does it take ail automobile traveling in...Ch. 3 - A moving walkway at an airport has a speed v1 and...Ch. 3 - A boy throws a baseball onto a roof and it rolls...Ch. 3 - You can use any coordinate system you like to...Ch. 3 - Towns A and B in Figure P3.35 are 80.0 km apart. A...Ch. 3 - In a local diner, a customer slides an empty...Ch. 3 - A father demonstrates projectile motion to his...Ch. 3 - Two canoeists in identical canoes exert the same...Ch. 3 - A rocket is launched at an angle of 53.0 above the...Ch. 3 - A farm truck travels due east with a constant...Ch. 3 - (a) If a person can jump a maximum horizontal...Ch. 3 - A ball is thrown straight upward and returns to...Ch. 3 - A home run is hit in such a way that the baseball...Ch. 3 - A 2.00-m-tall basketball player is standing on the...Ch. 3 - A quarterback throws a football toward a receiver...Ch. 3 - The x- and y-coordinates of a projectile launched...Ch. 3 - Spitting cobras can defend themselves by squeezing...Ch. 3 - When baseball outfielders throw the ball, they...Ch. 3 - A hunter wishes to cross a river that is 1.5 km...Ch. 3 - Chinook salmon are able to move upstream faster by...Ch. 3 - A daredevil is shot out of a cannon at 45.0 to the...Ch. 3 - If raindrops are falling vertically at 7.50 m/s,...Ch. 3 - A celebrated Mark Twain story has motivated...Ch. 3 - A landscape architect is planning an artificial...Ch. 3 - A golf ball with an initial speed of 50.0 m/s...Ch. 3 - Antlion larvae lie in wait for prey at the bottom...Ch. 3 - One strategy in a snowball fight is to throw a...Ch. 3 - A football receiver running straight downfield at...Ch. 3 - The determined Wile E. Coyote is out once more to...
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