PROBLEMS 5.1+ Another race. Veronica takes a 195-foot straightaway race at the constant speed of V= c.There is a clock at the start line, and a clock at the finish line, and Veronica wears a wristwatch. As Veronica passes the start line, her wristwatch and the start-line clock both ead zero. (The start- and finish-line clocks are synchronized in the Earth's frame.)
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- dx 4x 3. In so-called "natural units" (which is just a sneaky way to let us ignore a bunch of constants), the relativistic kinetic energy of a rigid body is given by the formula 1 КЕ — т V1 – v2 where m is the rest mass of the body and v is its relative speed. Alien scientists on a space station are observing an object falling into a black hole. As the object falls, it is disintegrating, losing mass at a rate of 3 (so its mass is changing at a rate of -3). How fast is the kinetic energy of the main part of the object changing when its mass is 20, its velocity is .7, and it is accelerating at a rate of .1 (remember that acceleration is the derivative of velocity with respect to time: a = dt 1Note that this formula does not make sense when v > 1. That is because in natural units, a speed of 1 corresponds to the speed of light, and nothing with positive rest mass can go that fast.A spaceship travels from the Earth to a star 13 light years away (as measured in the Earth’s frame). An astronaut on the ship says that the trip takes 16 years. What is the speed of the ship relative to the earth in m/s?As the drawing shows, a carpenter on a space station has constructed a 30.0° ramp. A rocket moves past the space station with a relative speed of 0.694c in a direction parallel to side x. What does a person aboard the rocket measure for the angle of the ramp? Number 30.0⁰ Units
- A rocket speeds by the earth at 0.77c. The earthlings measure the moving rocket to be 158 m long. What is the length of the rocket as measured by the passengers on the rocket? Please give your answer in meters. 247.63PROBLEMS 8.1. A trip to the grocery store. Tabetha needs to pick up bananas from a grocery store located 1200 feet from her home. She travels there at a speed of V = c. As she starts her journey, her wristwatch, her home's wall clock, and the grocery store's wall clock all read noon. (Tip: It will help to make four sketches: in the Earth's frame, leaving home and arriving at the store; in Tabetha's frame, leaving home and arriving at the store.) a. How much time elapses in the Earth's frame during her journey? b. How much time does Tabetha's wristwatch tick off during this journey? c. In Tabetha's frame, the grocery store moves toward her. How far must it travel to reach her? d. Using your result for part (c) and the definition speed = distance traveled time elapsed find out how much time it takes for the grocery store to reach Tabetha. Compare with your result from part (b).pion is an unstable sub-atomic particle commonly produced in high-energy physics experiments. How fast must a pion be moving on average to travel 25 m before it decays? The average lifetime, at rest, is 26.0 ns
- R3B2. 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?Playing a high-stakes game of basketball with a series of cartoon characters. The court has a total length of 28 meters measured in its own rest frame. The Street Sprinter, an animated lion on your team, can run at a maximum speed of ½ c. As measured in the rest frame of the court, a player on the opposing side throws a ball at ¼c from half court. At the same time, the Street Sprinter starts running at full speed from the full length of the court away. Call this time t=0. Draw a Space-Time diagram from the rest frame of the court with the Street Sprinter's initial position as the origin. Mark the following events on it, and find their spacetime coordinates (t,x) in the frame of the court and (t',x') in the frame of the Street Sprinter: A: The ball is thrown from half-court. B: The Street Sprinter takes off from the other side of the court C: The ball reaches the net D: The Street Sprinter reaches the net e) From the perspective of the referee in the court rest frame, does the ball…Imagine that you are going for a ride in a hot air balloon at the Canowindra Balloon Challenge. While the balloon is rising at a speed of 2.0 m/s, you throw a small ball down at a speed of 5.0 m/s relative to your body. A person who measures the ball's velocity at the instant of release will find that the ball's velocity relative to the ground at that instant is O a. 3.0 m/s, up. O b. 2.0 m/s, up. O c. 3.0 m/s, down. O d. 12.8 m/s, down. O e. 5.0 m/s, down.