An equilateral triangle with each side of length s is placed such that one of its sides is on the x axis of a coordinate system with the vertex opposite to this side on the y axis. Compute its interior angles in a frame that moves to the right of S (along the +ve x axis) with speed v. Is the sum of angles still 180º (take v = c/2 for example and confirm)?

Suppose two angry rhinoceros charge each other. According to a few observers on the ground, the rhinoceros on the left moved to the right at a speed of (1 - ϵ)c while the rhinoceros on the right moved to the left at a speed of (1 - ϵ)c. ϵ is in the range of 0 < ϵ < 1. How fast is the rhinoceros on the right moving in the frame of the rhinoceros on the left? (Show that this speed is less than c, no matter how small ϵ is)

Problem 3: A mass m is thrown from the origin att = 0 with initial three-momentum po in the y direction. If it is subject to a constant force F, in the x direction, find its velocity v as a function of t, and by integrating v find its trajectory. Check that in the non-relativistic limit the trajectory is the expected parabola. Hint: The relationship F = P is still true in relativistic mechanics, but now p = ymv instead of p = mv. To find the non-relativistic limit, treat c as a very large quantity and use the Taylor approximation (1+ x)" = 1 + nx when a is small.

A stationary observer O is standing on a platform of length 65 meters on earth. A rocket passes at a velocity of – 0.80c, parallel to the edge of the platform. The observer O notes that at a particular instant the front and back of the rocket simultaneously line up with the ends of the platform. (a) According to O, what is the time necessary for the whole rocket to pass a particular point on the platform? c = 3 × 10% m/s. (b) What is the rest length of the rocket according to an observer O' on the rocket? (c) According to O', what is the length of the platform? 65 m 0.8c O' Figure 2: Problem 4.

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.

Events 1 and 2 are exploding firecrackers that each emit light pulses. In the reference frame of the detector, event 1 leaves a char mark at a distance 3.40 m from the detector, and event 2 leaves a similar mark at a distance 2.10 m from the detector. If the two events are simultaneous in the reference frame of the detector and occur at instant t = 0, at what instant of time will each light pulse be detected?