00:03
A spaceship travels towards earth at the speed of, let's write it as v equals 0 .97c or the speed of light.
00:13
The occupants of the ship are standing with their torsos parallel to the direction of travel.
00:20
So if the spaceship is moving to the right, their torsos should be parallel to that direction.
00:29
According to earth, or observers from the earth, they are about 0 .50 meters in height and 0 .50 meters in width.
00:47
Now the question is, what are the occupants ' height and width according to others on the spaceship? so this is a problem of length contraction in relativistic motion, since the velocity is close to the speed of light, we'll consider it as relativistic.
01:09
Now, for length contraction, we have the formula of contracted length is equal to the proper length times 1 minus v squared over c squared.
01:27
Now, let's look at this in terms of the height first, so that is h is equal to h.
01:34
Not square of 1 minus b squared over c squared so the ones from earth are seen the contracted since they are on the observer from afar so this one is the contracted height and we are to solve for this proper height right here or the one being observed in the same location as the motion so this so get h0, we divide the equation by this factor right here...