The center of our Milky Way galaxy is about 23000 ly away. (a) To eight significant figures, at what constant speed parameter would you need to travel exactly 23000 ly (measured in the Galaxy frame) in exactly 25 y (measured in your frame)? (b) Measured in your frame and in lightyears, what length of the Galaxy would pass by you during the trip?

Particles called ?-mesons are created by accelerator beams. If these particles travel at 2.40 ✕ 108 m/s and live 3.00 ✕ 10−8 s when at rest relative to an observer, how long (in seconds) do they live as viewed in the laboratory?

If ever the human race would need to leave Earth, the Trappist-1 system might make a good destination – the star there has seven temperate terrestrial planets, a few of which are close to Earth’s size and mass. It’s 39.6 light years away, though, so it could take a long time to get there. (a) If the spaceship had a speed of 0.95c, how long would the journey take from the Earth’s reference frame? (b) How long would the journey be for the passengers on the spaceship?

The distance between two light pulses moving along the x-axis of the frame S is 2km. What is the distance between them from the point of view of an observer moving at a speed of 0.2c along the x-axis relative to S?

A spaceship from another galaxy passes over the solar system directly above a radial line from the sunto the Earth. (We measure the distance between the Earth and the Sun to be 1.496 x 1011 m.) Anobserver standing on the Earth measures that the spaceship is approaching at 0.800c. The Earth-basedobserver also measures that it takes the spaceship 625 seconds to travel from the sun to Earth. Ignorethe relative motion of the Sun and Earth in this problem – their relative speed is only 0.001c, negligiblysmall compared to 0.800c.a) According to a scientist in the spaceship, the Earth-Sun distance is: ______8.9 x 10 ^10__________________b) According to a scientist in the spaceship, the time it takes her to travel the Earth-Sun distance is:_________374 s _______________c) What is the ratio of the kinetic energy to rest energy of the spaceship? KE/ER = _______0.667__________d) As the spaceship passed over the Sun, the alien scientist launched a probe toward Earth, traveling at0.200c relative to…

A particle's dynamics are considered "relativistic" when its velocity is a significant fraction of the speed of light.  For example, the mass of a moving particle seen by a stationary observer increases in proportion to the square root of 1/(1 - (v/c)2).  For typical speeds in the everyday world it is not noticeable, but take a fast moving fundamental particle and you may have apparent mass increases or changes in its lifetime as a consequence of time dilation.   Look at this factor for the electron you measured at 100 V in the glass globe. Pick the best answer.     The effect is less than 0.1 %.     The effect is around 1%.     The effect is around 10%.     The effect is a factor of 2 change in mass.

The lifetime of a free neutron is 886 s. If a neutron moves with a speed of 2.57 ✕ 108 m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be (in s)?

An astronaut wishes to visit the Andromeda galaxy, making a one-way trip that will take 25.3 years in the space-ship's frame of reference. Assume the galaxy is 2.00 million light years away and his speed is constant. (a) How fast must he travel relative to Earth? The following approximation will prove useful: z 1 1 + x for x << 1. 2 - (Complete the equation for your answer.) (1-| C (b) What will be the kinetic energy of his spacecraft, which has mass of 1.08 x 10° kg? (c) What is the cost of this energy if it is purchased at a typical consumer price for electric energy, 13.0 cents per kWh?

In a parallel universe, the quantity t has the value 3.14049... Express a in that universe to (a) four significant figures: (b) five significant figures:

A new spaceship is created which can travel so fast that y=20. It travels from Earth to Andromeda. Estimate the distance measured by the astronaut inside the ship.