Is it possible to shoot a chicken in a minecart?
I've done some testing shooting a chicken in a minecart from directly above it, and I've had no luck hitting the chicken. It seems the hitbox of the minecart envelops the hitbox of the chicken. From my testing, the answer seems to be no, but I may be doing something wrong.
I ran a few simple tests, and it looks like no, you can't. The hitbox of the minecart completely swallows up the chicken, which becomes effectively invulnerable. You just end up breaking the minecart.