Carl is standing in a park 1000 m across. Rohan flies over the park at a very high speed, first passing over the east end of the park, and then passing over the west end. Carl and Rohan are discussing the time interval between when Rohan passed over the east end of the park and when he passed over the west end of the park. Who measured the proper time?

The international space station travels in orbit at a speed of 7.67 km/s. If an astronaut and his brother start a stop watch at the same time, on Earth, and then the astronaut spends 6 months on the space station, what is the difference in time on their stopwatches when the astronaut returns to Earth? Note that 6 months is about 1.577 x 10⁷ s, and c = 3 x 10 ⁸ m/s.

In the following figure, a right triangle is shown in its rest frame, S'. In the lab frame, S, the triangle moves with a speed v. How fast must the triangle move in the lab frame so that it becomes an isosceles triangle?