Relativistic length and time
6. Suppose two observers in different frames compare their meter sticks and their clocks.
a. Would both observers agree on their ranking for the lengths of each meter stick? Le, if
observr 1 sees a particular meter stick as being longer than the other, would observer 2 also
agree the second meter stick is longer?
b. Would the observers agree on their ranking for the rate at which each clock ticks?
The observers also measure the velocity of each other relative to their own frame.
c. How would the relative velocity measured by observer 1 compare to that measured by
observr 2?
d. In Galilean relativity, all observations between frames are symmetric: an observation made in
frame 1 of an event in frame 2 is the same as that made in frame 2 of an event in frame 1.
Are all observations in special relativity symmetric? If not, is there a subset that are?
]Player
Goal
7. A game of relativistic soccer is played in space. All players are in rockets that
travel at $c/4$, and all players can kick the ball at $c/2$ in their frame.
A player is travelling straight up, and when they are parallel with the goal they
kick the ball straight toward the center of the goal.
a. In the player's frame, in which direction relative to the x'-axis should they kick the ball?
(Hint: Draw a triangle involving the distance to the goal and the distance the goal has
travelled while the ball is moving.) Explain.
b. In the frame of the goal, the velocity of the ball is purely in the x-direction. How fast is the
ball traveling in the goal's frame?
c. Suppose all the players sped up to $c/2$. Would players have to be more accurate or less
accurate with their kicks?
Tutorials in Introductory Physics: Electrodynamics
Physics Education Group, University of Washington
Preliminary Edition, 2017
