Braking and motion-arrest apparatus for braking the arrival of a zipline cable rider at a landing platform and arresting the rider's motion to retain the rider at the platform. A frame is mounted on the cable to allow longitudinal rolling movement of the frame along the cable. A self-closing one-way latch is provided at the forward end of the frame. The latch includes a pair of capture plates which are normally inwardly biased toward one another, on opposite sides of the cable. The rider is tethered to a pulley block which rolls along the cable and collides with the latch. The collision force drives the plates laterally away from the cable, allowing the pulley block to roll through the latch. After the pulley block rolls past the latch, the plates' normal biasing closes the latch, preventing the pulley block from rolling back through the latch.