Get the bounds of the objects - i.e. baddie and plane, then check for intersection. In pseudo-code:
Rectangle rect_1 = plane.getBounds();
Rectangle rect_2 = baddie.getBounds();
if(rect_1.intersects(rect_2))
{
DoSomethingAmazing();
}
Here's a more detailed tutorial: http://zetcode.com/tutorials/javagamestutorial/collision/