You are flying on a plane. Your friend is on the ground. The lights on the wing of the plane blink at a specific interval. Which of you can measure the proper time of the blink?

Observer S detects two flashes of light. A big flash occurs at x1 = 1271 m and, slightly later, a small flash occurs at x2 = 492 m. The time interval between the flashes is Δt = t2 - t1. What is the smallest value of Δt for which observer S' will determine that the two flashes occur at the same x' coordinate?

A spacecraft flies past the earth in the direction toward the moon, a distance of 3.84 * 10^5 km. As measured by your clock on the earth, it takes 6.00 s for the clock on the spacecraft to tick off 2.00 s. You measure the length of the spacecraft in the direction of its motion to be 24.0 m. As measured by an astronaut at rest on the spacecraft, what are (a) the distance from the earth to the moon and (b) the length of the spacecraft?

Electromagnetic radiation from a star is observed with an earth-based telescope. The star is moving away from the earth with a speed of 0.580c. If the radiation has a frequency of 8.64 x 1014 Hz in the rest frame of the star, what is the frequency measured by an observer on earth?

A rocket travels along a line from the Sun to Saturn at a constant speed of 0.862c relative to the Sun. The distance from the Sun to Saturn is 1.43 x 1012 m, as measured by someone at rest with respect to the Sun. How long does the journey take (in minutes) as measured by an astronaut on the rocket? (Use c = 2.9979 × 108 m/s) min

Two spaceships, A and B, fly by a space station. An observer on the space station uses a telescope to measure the length of a meterstick in ship A and finds that it is 0.90 m . He does the same for ship B and finds that it is 0.60 m . What is the ratio of the speeds of the two ships relative to the space station, uBuA ?

Setup: A futuristic race from Earth to Alpha Centauri is taking place. But the winner of the race isn't who gets there first, it's who measures the smallest proper time along the way. The competitors start on Earth, from position (t, x) = (0, 0). They must travel from Earth (considered stationary) to Alpha Centauri, a distance of L = 4.37 light years away, such that they arrive at Alpha Centauri at Earth time of T = 10 years. Upon arrival, they compare their personal times (the proper time they measure along their whole trip) and the team with the smallest proper time wins. Question: a) Team A's spaceship immediately blasts off at (t, x) = (0, 0) and travels at a constant speed until they reach Alpha Centauri at Earth time of 10 years. Team B, on the other hand, have a much faster ship— they can travel so fast, you may consider their maximum speed to be the speed of light. Team B stays stationary on Earth for as long as they can; then, they blast off and travel at constant maximum…

A spaceship travels at a speed of 2.4 x 108 m/s. A clock in the spaceship passes 60 seconds. How much time (in second) passes on the clock at rest on the ground?

A particle has a rest mass of 7.15×10−27 kg and a momentum of 5.56×10−18 kg·m/s. Determine the total relativistic energy E of the particle.   Find the ratio of the particle's relativistic kinetic energy K to its rest energy ?rest.

The proper lifetime of a certain particle is 100.0 ns. How long does it live in the laboratory if it moves at v = 0.860c?