Can any object with positive mechanical energy collide earth?

Object with positive mechanical energy in an attractive force field moves along a hyperbolic path and whose energy is zero, moves along parabolic path...isn't it?...But why?...Can't any object with ve energy move along the line joining centre of force?...If its radial component of kinetic energy is greater than effective potential energy? Then? If I'm right then spacial object can collide earth....
Please ellaborate conceptually and help me out...
Thanks.