Show that if a body has speed v
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Show that if a body has speed v<c in one inertial frame, then v<c in every inertial frame. Hint: use displacement 4-vector dx = (c*dt,) where is the three-dimensional displacement in time dt.
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- In certain physical models, the nonhomogeneous term, or forcing term, g(t) in the equation ay" + by' + cy = g(t) may not be continuous, but have a jump discontinuity. If this occurs, a reasonable solution can still be obtained using the following procedure. Consider the following initial value problem. 240 if 0sts7T/6 y" + 4y' + 40y = g(t); y(0) = 0, y'(0) = 0, where g(t) = . if t> 7x/6 Complete parts (a) through (c) below. (a) Find a solution to the initial value problem for 0 sts 71/6. The solution for 0sts 7n/6 is y(t) = - 6 e -21 *cos 6t - 2 e - 2t sin 6t + 6 (Type an equation.) (b) Find a general solution for t> 71/6. The general solution for t> 7x/6 is y(t) = C, e-2 cos 6t + C, e -2t sin 6t (Type an equation. Do not use d. D. e, E, i, or I as arbitrary constants since these letters already have defined meanings.) (c) Now choose the constants in the general solution from part (b) so that the solution from part (a) and the solution from part (b) agree, together with their first…A person is traveling at 28.3 m/s due west on the highway and sees a tractor ahead of him moving ahead of him perpendicularly away from the road (North) at 6.50m/s. (Both these motions are relative to a frame at rest on the ground.) What is the car's velocity in the tractor's frame (magnitude and direction)?A frame B shown below in Figure 1, is rotated 90° about the z-axis, then translated 3 and 5 units relative to the n- and o-axis respectively, then rotated another 90° about the n-axis, and finally, 90° about the y-axis. Find the new location and orientation of the frame. (1,1,2) {B} F y a Figure 1 11
- 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?Calculate the interval ∆s2 between two events with coordinates ( x1 = 50 m, y1 = 0, z1 = 0,t1 = 1 µs) and (x2 = 120 m, y2 = 0, z2 = 0, t2 = 1.2 µs) in an inertial frame S. b) Now transform the coordinates of the events into the S'frame, which is travelling at 0.6calong the x-axis in a positive direction with respect to the frame S. Hence verify that thespacetime interval is invariant.