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Phy 3031 Modern physics, Spring 2008
Homework set #2. Due at the start of class on Monday, January 14, 2008.
1. Tarzan can swim through still water with a speed c 0 . To impress Jane, he swims
directly across (at a right angle to the shore) the Zambesi river and then returns to
his starting place. Where he is swimming, the Zambesi is a distance d wide, but flows
with a speed of v.
(a) How long does it take Tarzan to cross the river and then return?
(b) Jane appears bored by all of this, so now Tarzan decides to swim a distance d
directly upstream and then swim back downstream to the original spot on the
shore. How long does it take for Tarzan to make this round trip?
(c) What is the difference in these times in the limit that v ¿ c 0 ? This means:
subtract the two answers, and write your answer in terms of the small quantity
v/c 0 . Then take a Taylor expansion of the result, and keep only the dominant
term in powers of v/c 0
2. The current value of Hubble’s “constant” is about H = 72 (km/s)/Mpc, and the current
age of the universe is about 13.7 billion years. What was Hubble’s “constant” 106 years
after the big bang? Give your answer in units of (km/s)/Mpc . I am sure that you
recall from the first lecture that 1 pc ≈ 3 lt-yr, and that 1 Mpc = 106 pc. You can
verify these by googling “1 pc in light years”, for example.
3. Respond to the following question: If Einstein were to hold a mirror in front of himself
while running faster than the speed of light, then what would he see in the mirror?