Two clocks are synced on Earth. A ship takes one of the clocks during it journey and comes back. The clock on the ship is observed to run at a speed of only 2/5 that of a similar clock at rest on Earth. Calculate the velocity of the ship during its journey.
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A: t = t/v(1-v∧2/c∧2) 2.82 -1.02 =1.02/v(1-v∧2/c∧2) 1.8= 1.02/(1-v∧2/c∧2) (1-v∧2/c∧2) = 0.56 squaring…
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- As per special relativity time dilation could take place due to the velocity. If an object is moving very fast time measured in its frame of reference will be slower than the time measured in another frame of reference.
- The shortest time measured by the clock present at two events is called proper time. Thus using the proper time we get the formula for time dilation caused by velocity as,
Here ∆t' is the proper time, ∆t is dilated time, v is the relative velocity between the frames, and c is the speed of light.
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- There is a spaceship that moves past us with a speed of (3/5)c and it has a rest length of 1000 m. Two clocks on the ship's nose and tail have been synchronized with each other in the ship's frame of reference. (On the ground, we have many clocks that are synchronized with each other in our frame.) When the nose of the spaceship reaches us, both our clock as well as the clock in the ship's nose read t = 0. At this time (t = 0 to us), what will the clock in the ship's tail read and in what time will the tail reach us?Two atomic clocks are carefully synchronized. One remains in New York, and the other is loaded on an airliner that travels at average speed of 250 m/s and then returns to New York. When the plane returns, the elapsed time on the clock that stayed behind is 4.00 h. By how much will the readings of the two clocks differ, and which clock will show the shorter elapsed time?The starship Enterprise leaves a distant earth colony, which is nearly at rest with respect to the earth. The ship travels at nearly constant velocity toward earth. When the Enterprise reaches earth 1.10 y has elapsed, as measured on the ship. Clocks in the earth's reference frame show that the voyage lasted 2.73 y. How far from earth is the colony, as measured in the reference frame of the earth?(b) How far from earth is the colony, as measured in the reference frame of the ship?
- A spaceship leaves the solar system at v = (3/5)c and is headed towards a planet that is 20 c • years away (c is the speed of light). Assume the following: the Sun and the planet are mutually at rest and their clocks have been synchronized such that both read zero when the spaceship leaves. Say that the clock on the ship began at zero. If this is the case, then what should the clock on the ship read when it arrives at the planet?System S' has a velocity u = +0.33c relative to system S, as shown in the figure. The clocks of S and S' are synchronized at t = t' = 0 when the origins O and O' coincide. An event is observed in both systems. The event takes place at x = 672 m and at time t = 1.6 μs, as measured by an observer in S. What is the x'-coordinate of the event, measured by an observer in S'?Suppose 5 rocketships are all traveling in â in some frame S. The speeds are: St (min) 100 B 0 0.25 0.5 0.75 0.99 7 1 How much time passes on the clocks inside each rocketship if 100 minutes elapse on the stationary rocketship?
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- A spacecraft travels at 1.5 X 108 m/s relative to Earth. A process onboard the ship as measured by a stationary clock on Earth takes 85 min. How long would the same process take as measured by a clock onboard the ship?A spaceship carrying a light clock moves at a speed of 0.6c relative to an observer on Earth. If the clock on the ship advances by 1.00 s as measured by the space travelers aboard the ship, how long did that advance take as measured by the observer on Earth? O 1.15 s O 1.25 s O 3.6 s O 2.6 s O 0.96 s