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- In a certain particle accelerator, a proton has a kinetic energy that is equal to its rest energy. What is the speed of the proton relative to the accelerator? 0.87 c 0.25 c 0.75 c 0.71 c 0.50 c1. Taking north as positive and south as negative for all reference frames, suppose Mayor Adams is riding a southbound train to New York City traveling at 40 m/s relative to the ground, while Governor Hochul is riding a northbound train to Albany at 33 m/s relative to the ground. A) What is the velocity of Mayor Adams in Governor Hochul's reference frame (i.e. in the reference frame where Governor Hochul isn't moving)? B) What is the velocity of Governor Hochul in Mayor Adams reference frame? C) To his surprise Mayor Adams observes a groundhog running along the aisle towards the back of the train with a speed of 2 m/s relative to the train. What is the velocity of the groundhog in Governor Hochul's reference frame? D) What is the groundhog's velocity in the reference frame of someone standing at the train station? E) What is its velocity in Mayor Adams's reference frame? F) What is its velocity in the groundhog's frame? 30 10 ft. 5 ft. 15 ft.1) Calculate the interval As 2 between two events with coordinates (x1 = 50 m, y1 = 0, z1 = 0, t1 = 1 us) and (x2 = 120 m, y2 = 0, z2 = 0, t2 = 1.2 µs) in an inertial frame S. 2) Now transform the coordinates of the events into the S0 frame, which is travelling at 0.6c along the x-axis in a positive direction with respect to the frame S. Hence verify that the spacetime interval is invariant.
- The space and time coordinates for two events as measured in a frame S are as follows: Event 1: x1=x0 , t1=x0/c Event 2: x2=2x0, t2=x0/2c a. There exists a frame in which these events occur at the same time. Find the velocity of this frame with respect to S. b. What is the value of t at which both events occur in the new frame?B8] This question concerns two inertial frames S and S' with origins coinciding at t = t' = 0, and a set of events taking place along the x-axis, which defines the direction of relative motion. -8 a) The coordinates of event A in frame S are x = 12 m and t = 8x10 s. If the coordinates of this event in frame S' are x' = -3 m and t' = 7 x 10- s, show that the y factor for transformations between S and S' is 5/4. b) Events B and C take place in S' at a time t' = 6 × 10-* s at x' = 1 m and x' = 2 m respectively. What is their spatial separation in frame S? %3D -8- c) Event D takes place in S' at t' = 3 x 10 s and x' = 1 m. What is the time difference between events B and D in S? d) Is it possible for events A and D to take place at the same time in the frame of an observer moving along the x-axis?In an inertial reference frame S there is only a uniform electric field →, →→, = 8 kVm-¹. Find the magnitude of E' and B'in the inertial reference frame S' moving with a constant velocity v relative to the frame S at an angle a = 45° to the vector E. The velocity of the frame S' is 0-6 times the velocity of light c. E
- A train, which is 200 m long, approaches a tunnel, which is 120 m long. The train is moving at a velocity of 0.89 c. a. What is the length of the train as seen be someone standing at the entrance to the tunnel? m b. Is the train ever entirely inside the tunnel as seen be the observer at the entrance to the tunnel? ONLY 1 ATTEMPT IS ALLOWED FOR THIS PART. ---Select--- v c. What is the length of the tunnel as seen be a passenger on the train? m d. Is the train ever entirely inside the tunnel as seen by the passenger on the train? ONLY 1 ATTEMPT IS ALLOWED FOR THIS PART. ---Select--- vR3B2. Alicia is a student on a passenger train moving at a constant velocity relative to the ground. She synchronizes her watch with the station clock as she passes through the town of Bannon station, and then compares her watch with the station clock as she passes through the Center town station farther down the line. The ground is an inertial frame, and the Bannon and Center clocks are synchronized in that frame. (1) Using a model or diagram, is the time she measures between the events of passing through these towns a proper time? (2) Is it a coordinate time in some inertial reference frame? (3) Is it the spacetime interval between the events?