In general, catapulting is an act of throwing or hurling bodies over considerable distances, employing mechanical means only. Catapulting can be accomplished by a direct contact between bodies or with the help of physical fields (e.g., gravitational, electrical, magnetic). Direct catapult is a bounce of a body (particle) off another body (particle), assuming the mass or momentum of the bouncing body (particle) is small compared with the mass or momentum of the other body (particle). An interesting case of the non-contact catapulting is the gravity assist, a technique used in the design of interplanetary flights. Flybys of planets are used to either speed up the probes, or slow them down. For instance, the combined Cassini-Huygens spacecraft flew twice by Venus, once by Earth, and once by Jupiter, before it reached Saturn. Each flyby increased the spacecraft’s velocity. In order to solve simple cases of catapulting, we need to know relationships between the relevant quantities: linear momentum, angular momentum, kinetic energy, and potential energy. We wish to formulate problems that could be assigned to the students in secondary schools or to the participants in the physics competitions (Physics Olympiads). Solutions to such problems are interesting, unexpected, and always rewarding. Students learn to appreciate the presence of physical laws in the most common activities, particularly in sports (baseball, tennis, table tennis, football).