A spacecraft with a proper length of Lp passes by an observer on the Earth. According to this observer, it takes a time interval Δt for the spacecraft to pass a fixed point. Determine the speed of the object as measured by the Earthbased observer.

The origins of two frames coincide at t = t' = 0 and the relative speed is 0.994c. Two micrometeorites collide at coordinates x = 118 km and t= 191 us according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame S'? (a) Number i Units (b) Number i Units

1. You are an observer in a 100-m long spacecraft traveling from the earth to the moon at 0.8c. (a)What is the proper length of the spacecraft? (b) For a proper time interval of 1 sec., the relativistic time interval for the spacecraft measured from the earth reference frame would be: (c)Time dilation does not apply to all time-dependent physical and biological processes. T/F? (c) What is the relativistic length, DL measured from the reference frame of earth? (d) An APOLLO crew left a flat mirror reflector on the surface of the moon (for all you deniers out there, in the 50th anniversary year of APOLLO 11!). If the average surface-to-surface distance from the earth to the moon is 3.83 x 10^8 m, then how long does it take moonlight to reach earth?

a) Find the value of y for the following situation. An astronaut measures the length of his spaceship to be 100 m, while an earthbound observer measures it to be 25 m. b) What is the speed of the spaceship relative to Earth?

At Brookhaven National Laboratory in New York, atomic nuclei are accelerated to 99.995% of the ultimate speed limit of the universe—the speed of light, c. Compared to the kinetic energy of a nucleus moving at 99.000% of c, the kinetic energy of the same nucleus moving at 99.995% of c is about (i) 0.001% greater; (ii) 0.1% greater; (iii) 1% greater; (iv) 2% greater; (v) 16 times greater.

A car traveling at 35.0 m/s takes 26.0 minutes to travel a certain distance according to the driver’s clock in the car. How long does the trip take according to an observer at rest on Earth? Hint: The following approximation is helpful:

You have been posted to a remote region of space to monitor traffic. Near the end of a quiet shift, a spacecraft streaks past. Your laser-based measuring device reports the spacecraft’s length to be 85 m. The identification transponder reports it to be the NCXXB-12, a cargo craft of proper length 100 m. In transmitting your report to headquarters, what speed should you give for this spacecraft?

A futuristic rocket ship of mass m,hip = 6.0 × 10° kg is sent into space carrying one person with the goal of traveling to nearby stars. The ship uses a newly discovered matter-antimatter drive that converts matter into energy at 100% efficiency. We will take Earth as the rest frame. For parts (a) through (d) you are interested in the portion of the spaceship's travel where it is using its drive to convert matter into the kinetic energy of the ship. (a) What is the speed of the ship when the work done by the ship's drive is equal to 150,000 TWh (the total energy used by humanity in 2014)? (b) How much work must the drive do for the rocket to reach a final speed of 0.95c? (c) How much matter would the drive need to annihilate in order for the ship to reach the final speed of 0.95c? Assume that the matter used in the antimatter drive is collected from the interstellar medium and that the mass of the ship remains constant. (d) When at the final speed of 0.95c, by what factor is the ship's…

The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a reference frame in which the muons are stationary, if the number of muons at t = 0 is N0, the number at time t is given by , where τ is the mean lifetime, equal to 2.2 ms. Suppose the muons move at a speed of 0.95 c and there are 5.0 × 104 muons at t = 0. (a) What is the observed lifetime of the muons? (b) How many muons remain after traveling a distance of 3.0 km?

A particle has a rest energy of 4.31×10−13 J and a total energy of 8.33×10−13 J. Calculate the momentum p of the particle.