Question

Spaceman Spiff overflies the earth 4 times as you observe him. For each of the velocities below calculate how long and how tall Spaceman Spiffs spaceship will appear to be to you if he measured it as 100 m in length and 10 m in height just before he overflew the earth.

Velocity	Length	Height
.25 c	93.75 m	10 m
.50 c	75 m	10 m
.8 c	36 m	10 m
.95 c	9.75 m	10 m

Answer 1

Using length contraction formula ,

L = L_o

Where, L =the observed length

  L_o = the proper length

  v = velocity

c = speed of light

As we know, length contraction is only in the direction in which the object is travelling.So, length contraction will be observed only in the length of the spaceship,not in it's height.

So, Height =10 m for all four cases.

For v = 0.25 c,

L = 100 x = 100 x 0.968 m = 96.8 m

For v = 0.50 c,

L = 100 x = 100 x 0.866 m = 86.6 m

For v = 0.8 c,

L = 100 x = 100 x 0.6 m = 60 m

For v = 0.95 c,

L = 100 x = 100 x 0.312 m = 31.2 m