A spaceship, 250 m long as seen on board, moves by the earth at 0.900c. What is its length (in m) as measured by an earth-bound observer?

A 1 km spacecraft is racing towards the Sun at 0.75c. Using equations given in class, calculate the spacecraft length you measure from Earth. Treat Earth as not moving compared to the spacecraft's motion of 0.75 c.

A UFO streaks across a football field at 0.90c relative to the goal posts. Standing on the field, you measure the length of the UFO to be 228 m. The UFO later lands, allowing you to measure it with a meter stick. What length do you now obtain?

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?

A spaceship moves past Earth with a speed of 0.808c. As it is passing, a person on Earth measures the spaceship's length to be 78.7 m. HINT (a) Determine the spaceship's proper length (in m).  m (b) Determine the time (in s) required for the spaceship to pass a point on Earth as measured by a person on Earth.  s (c) Determine the time (in s) required for the spaceship to pass a point on Earth as measured by an astronaut onboard the spaceship.  s

How far from the earth would you be able to travel in a lifetime of 88 years if you were able to travel at a constant speed of 0.67c?

A rocket launched outward from Earth has a speed of 0.38c relative to the Earth. The rocket is directed toward an incoming meteor that may hit the planet. If the meteor moves with a speed of 0.70c relative to the rocket and directly toward it, what is the speed of the meteor as observed from Earth?

Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has a velocity v= 0.980c. The muon then travels at constant velocity and lives 1.52 us as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock. See the figure below. Enter your answers to at least four significant figures. Assume the speed of light is 2.998 x 108 m/s.) اد us At (a) How long (in us) would the muon have lived as observed on the Earth if its velocity was 0.0690c? (b) How far (in m) would it have traveled as observed on the Earth? (c) What distance (in m) is this in the muon's frame?

The starship Enterprise approaches the Klingon home world with speed 0.6c relative to the planet. To announce its arrival, the Enterprise sends a message in a projectile that travels toward the planet with speed 0.4c relative to the Enterprise. At what speed does Klingon at the surface of the planet see the projectile approach?  Using relativistic velocity equation.

A particle whizzes through your lab at a speed of 0.74c. Your detectors determine that its lifetime was 1.1ns. Find its lifetime in the particle's reference frame. Please give your answer in nanoseconds.