If you stood with the Earth directly overhead and pitched the rock at the horizon due east at 1730 + 680 = 2410 m/s (which would be mach 7 back on Earth), its trajectory would depress down into the Earth's atmosphere. Assuming this rock is small enough to hold, there's no way it's making it to the ground though. Even if it barely scraped the upper atmosphere over a dozen passes and slowed until its orbit became circular, eventually it would dig its heels in under 120 km or so and burn up. If you cast it in a big blob of epoxy mixed with fiberglass it might make it down. When Apollo crew did their 680 m/s trans Earth injection they'd wind up with a perigee of only 50 km.