I'm new to radar. please excuse my question if it doesn't make sense to you. 

In a pulsed radar signal, why is the required sampling frequency "2 times the inverse of pulse width" instead of "2 times the carrier center frequency"?

Consider a 100 ms pulse width and a 1000 Hz carrier frequency, i.e. there are 100 cycles of sinusoidal waves per pulse width. 

If I use a sampling frequency of 2/(0.1 s), what would I get in the spectrum plot? 

Also, is this sampling frequency (2\*1/pulseWidth) the same as the fast time sampling frequency?