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## Homework Statement

**The proper length of spaceship A is 60.0m and the proper length of spaceship B is 120.0m. The proper mass of spaceship A is 15000 kg. An observer on earth watches the two spaceships fly past at a constant speed and determines that they have the same length. If the speed of the slower ship is 0.70c, find:**

a-The speed of spaceship B, relative to an observer on earth

a-The speed of spaceship B, relative to an observer on earth

b-

**The mass of spaceship A, relative to an observer on earth**

2. Homework Equations

2. Homework Equations

γ = 1/ √1- v

^{2}/ c

^{2}

m

_{m}= m

_{s}/ √ 1- v

^{2}/ c

^{2}

## The Attempt at a Solution

**a)**

Use the Lorentz factor to determine the velocity of ship B

γ = proper length B/ contracted length A

γ = 120m /42.8m

γ = 2.8

γ = 1/ √1- v

^{2}/ c

^{2}

rearrange to solve for v.

γ

^{2}= 1/ √1- v

^{2}/ c

^{2}

1 - v

^{2}/ c

^{2}= 1/γ

^{2}

v

^{2}/ c

^{2}= 1 - 1/γ

^{2}

v/c = √1- 1/2.8

^{2}

v/c = √1- 1/7.84

v = 0.934

The speed of spaceship B, relative to an observer on Earth will be 0.934c.

b) The mass of spaceship A, relative to an observer on earth. 3mk

m

_{m}= m

_{s}/ √ 1- v

^{2}/ c

^{2}

m

_{m}= 15000kg / √1- 0.70c

^{2}/ c

^{2}

m

_{m}= 15000kg / √1- 0.49

m

_{m}=2100.4

The mass of spaceship A, relative to an observer on Earth, is 2100kg.

The main part I am unsure of is question a, I hadn't specifically been taught about the Lorentz Factor, but this is all I could find that seemed to be able to determine the answer. As such I am not sure if I applied it correctly. If someone could give a few pointers that would be great.