Alice and Mary are twins. Mary moves away from the Earth to a distant planet 12 light years away from the Earth. a) With what MINIMUM speed should Mary move in order to return to the Earth N=6 years younger than her sister? b) Explain the resolution of "twin paradox"? ( The twins seem to be in a symmetrical situation, why is one of them younger.)
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- Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.82c. The muon then travels at constant speed and lives 1.5 μs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.) 1)how many meters does it travel as observed on the earth? 2)how many meters is this in muon's frame?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? (a) Number (b) Number I Units Units1. A supertrain of proper length 195 m travels at a speed of 0.92c as it passes through a tunnel having proper length 90.0 m. How much longer is the tunnel than the train or vice versa as seen by an observer at rest with respect to the tunnel? meters
- a) b) 6. 6. a) 6. b) 6. c) (Barn-pole paradox) As shown in the figure below, a barn with a (resting) width of w = 5.0m is at rest on the ground. A pole with a resting length of 1 = 6.0m is flying towards the barn at a fast speed of 0.8c relative to the barn. (c denotes the speed of light.) Calculate the length of the pole as measured by an observer that is at rest with the barn (standing on the direction of motion of the pole). Calculate the width of the barn as measured by an observer that is at rest with the pole (sitting on the pole and flying towards the barn). From your calculations for parts (a) and (b), it is evident that the observer on the ground thinks that the pole can fit in the barn, while the observer on the pole thinks that the pole cannot fit in the barn. Suppose that the barn is equipped with automatic front and back doors. Use the relativistic nature of simultaneity to explain the barn-pole paradox: can the front and back doors momentarily trap the pole in the barn…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?A borg spaceship is in the shape of a cube of side 100.0 m when it is at rest with respect to an observer. What length, width, and height will be the observer witness if the ship flies by at 0.62c going right to left? b) two borq crewmembers are arm wrestling, and it takes 6.0 seconds for the contest to end as measured by a third crewmember. As the ahip flies past the earth at 0.62c, how long will the match last according to an observer on earth?
- Please answer D A spaceship from another galaxy passes over the solar system directly above a radial line from the sun to the Earth. (We measure the distance between the Earth and the Sun to be 1.496 x 1011 m.) An observer standing on the Earth measures that the spaceship is approaching at 0.800c. The Earth-based observer also measures that it takes the spaceship 625 seconds to travel from the sun to Earth. Ignore the relative motion of the Sun and Earth in this problem – their relative speed is only 0.001c, negligibly small compared to 0.800c. a) According to a scientist in the spaceship, the Earth-Sun distance is: 8.976 x 1010m b) According to a scientist in the spaceship, the time it takes her to travel the Earth-Sun distance is: 357s 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 at 0.200c relative to the spaceship. What would the…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?1. Suppose a spaceship heading straight toward the Earth at 0.650c can shoot a canister at 0.400c relative to the ship. (a) What is the velocity of the canister relative to Earth, if it is shot directly at Earth? (b) If it is shot directly away from Earth?
- An observer measures a spacecraft’s length to be exactly half of its rest length. a) What is the speed of the ship relative to the observer’s frame of reference? b) By what factor do the spaceship’s clocks run slow relative to clocks in the observer’s frame?4. In a colliding beam apparatus, two beams of protons are aimed at each other. The first proton moves with a speed of 0.70c to the right; the second moves with a speed of 0.90c to the left. Both speeds are measured relative to the laboratory frame of reference. What is the speed of the second proton relative to that of the first? ooflPlease please please answer everything super super fast please