Youtube video won't play with Firefox but will with Safari! What can I do to solve this problem ?

On the same iMac, there are several accounts. For one of them, Youtube videos won't play in Firefox, but will with Safari. For the other accounts, Firefox and Safari can play Youtube videos!?

Any hint where I can search to solve the issue ?

EDIT : I'm sorry. I can not flag anything because this long lasting (several months) problem has been solved, and I don't know how! I didn't change anything. This must be a side effect of something I did. Probably on my Admin Account. The mystery stays forever...
If you don't have Adobe Flash plugin installed you need to do so and give it another go.
Do you have by any chance the Firefox "Flashblock" extension installed?!