H3 Time Dilation, Length Contraction

1. A space 100m long space ship travels to planet X which is a distanace of 6E11m from Earth. It travels at 90% of the speed of light. How long will this journey take according to the observer on the earth?

1111s

2222s

3333s

4444s

The journey from Earth to planet X is a distance of 6E11m. The space ship is traveling at 90% of the speed of light. According to the theory of relativity, time dilation occurs when an object is moving at high speeds. This means that time appears to pass more slowly for the moving object compared to a stationary observer. Therefore, the journey will take longer according to the observer on Earth. To calculate the time it takes for the journey, we can use the formula t = d/v, where t is the time, d is the distance, and v is the velocity. Plugging in the values, we get t = (6E11m) / (0.9c), where c is the speed of light. Solving this equation gives us a time of approximately 2222 seconds.

Explanation

The journey from Earth to planet X is a distance of 6E11m. The space ship is traveling at 90% of the speed of light. According to the theory of relativity, time dilation occurs when an object is moving at high speeds. This means that time appears to pass more slowly for the moving object compared to a stationary observer. Therefore, the journey will take longer according to the observer on Earth. To calculate the time it takes for the journey, we can use the formula t = d/v, where t is the time, d is the distance, and v is the velocity. Plugging in the values, we get t = (6E11m) / (0.9c), where c is the speed of light. Solving this equation gives us a time of approximately 2222 seconds.

2. A space 100m long space ship travels to planet X which is a distanace of 6E11m from Earth. It travels at 90% of the speed of light. What is the value to 2dp of the Lorentz factor (gamma)

1.2

2.3

3.4

4.5

The Lorentz factor (gamma) is a term used in special relativity to describe the time dilation and length contraction experienced by objects moving at relativistic speeds. It is given by the equation gamma = 1/sqrt(1 - (v^2/c^2)), where v is the velocity of the object and c is the speed of light. In this question, the spaceship is traveling at 90% of the speed of light. Plugging this value into the equation, we find that gamma is approximately 2.3 when rounded to 2 decimal places.

Explanation

The Lorentz factor (gamma) is a term used in special relativity to describe the time dilation and length contraction experienced by objects moving at relativistic speeds. It is given by the equation gamma = 1/sqrt(1 - (v^2/c^2)), where v is the velocity of the object and c is the speed of light. In this question, the spaceship is traveling at 90% of the speed of light. Plugging this value into the equation, we find that gamma is approximately 2.3 when rounded to 2 decimal places.

3. A space 100m long space ship travels to planet X which is a distanace of 6E11m from Earth. It travels at 90% of the speed of light. Who measures the proper length of the journey from Earth to Planet X?

Pilot on space ship

Observer on the Earth

Independent observer

Great Galactic time measurer

The observer on Earth measures the proper length of the journey from Earth to Planet X. Since the observer on Earth is stationary and not moving at relativistic speeds, they can accurately measure the distance between Earth and Planet X. On the other hand, the pilot on the spaceship is moving at a high velocity and time dilation effects come into play, causing the length of the journey to appear shorter for the pilot. An independent observer or a Great Galactic time measurer may not have the necessary frame of reference to accurately measure the distance.

Explanation

The observer on Earth measures the proper length of the journey from Earth to Planet X. Since the observer on Earth is stationary and not moving at relativistic speeds, they can accurately measure the distance between Earth and Planet X. On the other hand, the pilot on the spaceship is moving at a high velocity and time dilation effects come into play, causing the length of the journey to appear shorter for the pilot. An independent observer or a Great Galactic time measurer may not have the necessary frame of reference to accurately measure the distance.

4. A space 100m long space ship travels to planet X which is a distanace of 6E11m from Earth. It travels at 90% of the speed of light. Calculate the distnace from Earth to Planet X according to the travelling spaceship?

6E11m

3.31E11m

2.61E11m

1.42E11m

1.21E11m

Since proper length is measured by observer on Earth,
Length = properlength/gamma
Length = 6E11/2.3

Explanation

Since proper length is measured by observer on Earth,
Length = properlength/gamma
Length = 6E11/2.3

5. A space 100m long space ship travels to planet X which is a distanace of 6E11m from Earth. It travels at 90% of the speed of light. Who measures proper time for the journey?

Observer on the earth

Pilot of space ship

Another independent observer

The cosmic time keeper

must be the pilot of the space ship since the start and the finish of the journey to him occur at the same place (where he is)

Explanation

must be the pilot of the space ship since the start and the finish of the journey to him occur at the same place (where he is)

6. A space 100m long space ship travels to planet X which is a distanace of 6E11m from Earth. It travels at 90% of the speed of light. Calculate the time taken for the voyage according to the pilot of the space ship.

1111s

966s

822s

733s

544s

since space ship measures proper time,
time = gamma x proper time
proper time = time/gamma
=2222.22/2.3

Explanation

since space ship measures proper time,
time = gamma x proper time
proper time = time/gamma
=2222.22/2.3