The photodissociation of (fluorinated) alkyl iodides in helium nanodroplets at a wavelength of 266 nm has been investigated by means of ion imaging techniques. It is found that a significant fraction of the created fragments escapes from the helium droplets. The speed and kinetic energy distributions of these fragments are found to be notably modified with respect to the corresponding gas phase distributions. The fragments, furthermore, show a speed dependent angular distribution. The loss of kinetic energy as well the reduction of the anisotropy parameter show a strong mass dependence. These observations point to a non-thermal escape process in which the kinetic energy and momentum transfer from the fragments to the solvent is governed by binary collisions with the individual helium atoms making up the droplet. Monte Carlo simulations based on hard sphere binary collisions substantiate this interpretation of the data.