A girl is strapped to a board that is moving so that gamma along the length of the board is 2.0. The board and direction of relativistic motion is along the horizontal. You are standing next to a hole on a horizontal platform that she hopes to pass through (with the board's length parallel to the platform) when she arrives. The board has length L in her reference frame. The diameter of the hole is 0.75L in your reference frame. (For the purpose of this problem, you can neglect the vertical component of the movement necessary for her to pass through the hole.)
a) What is the length of the girl's board in your reference frame when she arrives? Does she pass through?
b) What is the diameter of your hole in her frame when she arrives? Can she pass through?
c) Given that you witnessed her passing through the hole, she must have passed through in her reference frame, as well. How?