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Chapter 12: Q10P (page 518)

Short Answer

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01

Expression for the vertical and horizontal component of length:

02

Determine the angle observed by an observer on the dock:

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Most popular questions from this chapter

Why can’t the electric field in Fig 12.35 (b) have a, z component? After all, the magnetic field does.

Suppose you have a collection of particles, all moving in the x direction, with energies E1,E2,E3,............. and momentap1,p2,p3,............... . Find the velocity of the center of momentum frame, in which the total momentum is zero.

Every years, more or less, The New York Times publishes an article in which some astronomer claims to have found an object traveling faster than the speed of light. Many of these reports result from a failure to distinguish what is seen from what is observed—that is, from a failure to account for light travel time. Here’s an example: A star is traveling with speed v at an angleθto the line of sight (Fig. 12.6). What is its apparent speed across the sky? (Suppose the light signal fromb reaches the earth at a timelocalid="1656138453956" ∆tafter the signal from a, and the star has meanwhile advanced a distancelocalid="1656138461523" ∆sacross the celestial sphere; by “apparent speed,” I meanlocalid="1656138468709" (∆s/∆t). What anglelocalid="1656140989446" θgives the maximum apparent speed? Show that the apparent speed can be much greater than c, even if v itself is less than c.

Consider a particle in hyperbolic motion,

x(t)=b2+(ct)2,y=z=0

(a) Find the proper time role="math" localid="1654682576730" τas a function of τ, assuming the clocks are set so thatτ=0 whenτ=0 . [Hint: Integrate Eq. 12.37.]

(b) Find x and v (ordinary velocity) as functions ofτ .

(c) Findημ (proper velocity) as a function of τ.

A neutral pion of (rest) mass mand (relativistic) momentum p=34mcdecays into two photons. One of the photons is emitted in the same direction as the original pion, and the other in the opposite direction. Find the (relativistic) energy of each photon.
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