A spaceship whose rest length is 432 m has a speed of 0.85c with respect to a certain reference frame. A micrometeorite, also with a speed of 0.85c in this frame, passes the spaceship on an antiparallel track. How long does it take this object to pass the spaceship as measured on the ship?
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- A1. (a) A large rocket ship traveling away from Earth at a speed of 0.4c launches a shuttle which also travels in the direction away from earth. From an observer on the rocket ship the shuttle is receding at a speed of 0.6c. Calculate the velocity of the shuttle for an observer on Earth. (b) A spaceship leaves Earth and travels in a fixed direction with constant speed 0.80c in the Earth's reference frame. A video call is set to be made from the spaceship exactly one year after launch, as measured by a clock on the spaceship. (i) Calculate how far away from Earth the spaceship is (in light-years) when the video call is made. (ii) Calculate how long after the departure time, as measured on Earth, before the video call is received on Earth. The call is transmitted by radio waves.A spaceship travels from Mercury to Mars at a speed of 0.81c relative to the Earth. Assume Earth, Mars and Mercury don’t move relative to each other. The time of the trip as measured by an Earth observer is 700 seconds. W What is the distance between Mercury and Mars as measured by a passenger on the spaceship?A spaceship travels at 0.818c relative to Earth. If the spaceship fires a small rocket in the forward direction, how fast (relative to the ship) must it be fired for it to travel at 0.870c relative to Earth?
- Twins who are 19.0 years of age leave the earth and travel to a distant planet 12.0 light-years away. Assume that the planet and earth are at rest with respect to each other. The twins depart at the same time on different spaceships. One twin travels at a speed of 0.905c, and the other twin travels at 0.407c. (a) According to the theory of special relativity, what is the difference between their ages when they meet again at the earliest possible time? A₂-A₁ = (b) Which twin is older?The inertial reference frames, S and S', both share the same origin at t = t'= 0. The 5' trame is moving at a speed 0.700c in the positive direction, as seen by frame S. An event happens at (1', x', y', z') = (300s, 2.50×10m,1.50×10"m, 2.90x10"m), as observed in the S' frame. What are the spacetime coordinates in the S frame?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
- 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.1. Consider inertial reference frame S to be the lab frame. A proton is moving in the positive x (+x) direction at a kinetic energy of 1250 MeV, as measured in frame S. Inertial reference frame S' moves at a speed of 0.55c in the positive-x (+x) direction relative to frame S. a) Find the speed of the proton in terms of the speed of light, c, as measured in frame S. b) Find the magnitude and direction of the speed of the proton as measured in frame S'.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?
- A spacecraft has a speed of 0.4c relative to Earth. As measured on Earth, the elapsed time between two events that happen at the same location on Earth is 4 h. Determine what the elapsed time between those two events would be from the spacecraft's frame.An alien spaceship traveling at 0.560c toward the Earth launches a landing craft. The landing craft travels in the same direction with a speed of 0.760c relative to the mother ship (as measured by aliens on the mother ship). As measured on the Earth, the spaceship is 0.130 ly from the Earth when the landing craft is launched. (a) What speed do the Earth-based observers measure for the approaching landing craft? 0.926 C (b) What is the distance to the Earth at the moment of the landing craft's launch as measured by the aliens (mother ship)? 0.108 ly (c) What travel time is required for the landing craft to reach the Earth as measured by the aliens on the mother ship? 0.19 Your response differs from the correct answer by more than 100%. yr (d*) What travel time is required for the landing craft to reach the Earth as measured by Earth-based observers? yr (e*) What travel time is required for the landing craft to reach the Earth as measured by those on the landing craft? yrThree polarizing sheets are placed in a stack with the polarizing directions of the first and third perpendicular to each other. What angle should the polarizing direction of the middle sheet make with the polarizing direction of the first sheet to obtain maximum transmitted intensity when unpolarized light is incident on the stack? 0° 15° 30° 45° 60° 75° 90°