Consider British Airways as an example. Their website provides a list of car seats requirements and one of them is:
must be designed to be secured by means of a normal aircraft single lap strap ...
Therefore, it looks like you need to buy a car seat which meets the requirements or to check rules of your airline (if it is not British Airways).
However, returning to British Airways, the different section of the same page states:
If your infant is less than two years old and you haven't reserved a carrycot position, your infant can sit on your lap using an extension seat belt. The cabin crew will provide this for you and show you how to use the seat belt.
It looks like this additional seat belt is measure against, as you said, "a kid turning into a projectile".