We study projectile motion with air resistance quadratic in speed. An approximation of a low-angle trajectory is considered where the horizontal velocity, v x , is assumed to be much larger than the vertical velocity, v y . The explicit solutions for the range and flight time are expressed in terms of the secondary branch of the Lambert function, . In addition to their theoretical importance, the results obtained will be of interest to teachers involved in undergraduate physics courses.

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Particular defect structures appear during directional solidification of the Al(fcc)-Al 2 Cu(q) lamellar eutectic composite, the so-called lamellar faults. Each fault corresponds to terminations of Al and q lamellae. These terminations consist of a continuous succession of three types of ribbon-like interfaces, among which two are low angle boundaries: one is located in the fcc phase and the other in the q intermetallic (C16 standard type, a = 0.6063 nm, c = 0.4872 nm). High resolution transmission electron microscopy (HRTEM) of a q/q low angle tilt boundary with an electron beam parallel to h113iq shows that the core structures of the dislocations are undissociated despite the large magnitude of the possible Burgers vectors. The dislocations are of mixed-type character and oriented along the h113iq direction the closest to the growth axis direction of the eutectic. An unusual defect present in the tilt boundary consists of a dense group of three dislocations separated by nanometric distances. This defect acts like a single dislocation at far field distance. The mechanical equilibrium of such a defect has been studied using isotropic and anisotropic elasticities. It is strongly suggested that two of these dislocations form a dipole, which would indicate that the boundary has not a completely relaxed structure.