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Chapter 36: Q. 56 (page 1061)

A rocket fires a projectile at a speed of 0.95c while traveling past the earth. An earthbound scientist measures the projectile’s speed to be 0.90c. What was the rocket’s speed as a fraction of c?

Short Answer

Expert verified

The speed of rocket is 0.34 c.

Step by step solution

01

Given information

We have given that, a rocket fires a projectile at a speed of 0.95c while traveling past the earth. An earthbound scientist measures the projectile’s speed to be 0.90c.

02

Step 1.

Let the earth’s frame of reference is S and the rocket’s frame of reference is S ′. Speed of projectile while passing earth u = 0.95 c and speed of projectile observed by scientist in earth's frame of reference u' = 0.90 c.

03

Step 2. 

Using Lorentz velocity transformation equation to calculate the speed of rocket :

v=u-u'1-uu'c2

v=0.90c-0.95c1-(0.90c)(0.95c)c2

v=0.34c.

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Most popular questions from this chapter

Teenagers Sam and Tom are playing chicken in their rockets. As FIGURE Q36.2 shows, an experimenter on earth sees that each is traveling at 0.95cas he approaches the other. Sam fires a laser beam toward Tom.

a. What is the speed of the laser beam relative to Sam?

b. What is the speed of the laser beam relative to Tom?

The nuclear reaction that powers the sun is the fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply 4p→He4+Energy. The mass of a proton, to four significant figures, is 1.673×10-27kg, and the mass of a helium nucleus is known to be 6.644×10-27kg.

a. How much energy is released in each fusion?

b. What fraction of the initial rest mass energy is this energy?

A 1.0g particle has momentum 400,000kgm/s. What is the particle’s speed in m/s?

The sun radiates energy at the rate 3.8×1026W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0×1030kg.

a. How much mass does the sun lose each year?

b. What percent is this of the sun’s total mass?

c. Fusion takes place in the core of a star, where the temperature and pressure are highest. A star like the sun can sustain fusion until it has transformed about 0.10%of its total mass into energy, then fusion ceases and the star slowly dies. Estimate the sun’s lifetime, giving your answer in billions of years.

Derive the Lorentz transformations for tand t'.

Hint: See the comment following Equation 36.22.
See all solutions

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