The following six problems are about the following situation: A spaceship at res

Question

The following six problems are about the following situation: A spaceship at rest on the earth has a length of 120 m and a mass of 16,000 kg. Then the spaceship begins to move away from the earth at 3/4 the speed of light.

10)  How long do observers ON THE SPACESHIP measure the spaceship to be?

79 m

120 m

182 m

11)  How long do observers ON EARTH measure the spaceship to be?

79 m

120 m

182 m

12)  When 10 years have passed ON EARTH, how much time do observers ON EARTH measure the spaceship's clocks to have moved through?

6.6 yr

10.0 yr

15.1 yr

13)  What do observers ON EARTH measure the spaceships momentum to be?

2.4 x 1012 kg-m/s

3.6 x 1012 kg-m/s

5.4 x 1012 kg-m/s

14)  If the spaceship sends out a second ship away from the earth at what observers ON THE SPACESHIP think is 1/2 the speed of light, how fast do the observers ON EARTH think the second ship is moving?

0.47c

0.78c

0.91c

1.00c

1.25c

15)  If the spaceship sends out a second ship toward the earth at what observers ON THE SPACESHIP think is 9/10 the speed of light, how fast do the observers ON EARTH think the second ship is moving?

-0.15c

-0.31c

-0.46c

-0.65c

-1.00c

Explanation / Answer

Given,
length of the spaceship = 120 m
mass = 16000 kg
speed of spaceship = 3 * c / 4
observers ON THE SPACESHIP measure the spaceship to be 120 m Answer
observers ON EARTH measure the spaceship to be = length * sqrt(1 - (v/c)^2)
observers ON EARTH measure the spaceship to be = 120 * sqrt(1 - (3/4)^2)
observers ON EARTH measure the spaceship to be = 79 m
Time = T0 / sqrt(1 - (v/c)^2)
10 = T0 / sqrt(1 - (3/4)^2)
T0 = 6.6 year
When 10 years have passed ON EARTH, the time observers ON EARTH will measure = 6.6 years Answer
observers ON EARTH measure the spaceships mass = m0 / sqrt(1 - (v/c)^2)
observers ON EARTH measure the spaceships mass = 16000 / sqrt(1 - (3/4)^2)
observers ON EARTH measure the spaceships mass = 24189.726 kg Answer
momentum = mass * velocity
momentum = 24189.726 * 3 * c / 4
observers ON EARTH measure the spaceships momentum to be = 5.4 * 10^12 kg-m/s Answer

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