Look at a "normal" lunar mission such as Prospector. It was a 105 hour transit. I mention Prospector because it did in fact hit a target on the moon.
So, what if a strike was not a launch of a new missile for the purpose, but was crashing a craft that was already in Lunar orbit for some purpose or another? Such a craft might have a 2-hour orbit, so if a decision was made to de-orbit a probe that was near end-of-life anyway, with the realization that it could be aimed at the right location, there might be up to a 2-hour latency for it to cycle around to the right place to dive from. Then it doesn't just drop instantly, but the burn lowers the opposite side so figure less than half an orbit more to intersect the ground.
Note that orbital probes are often crashed on purpose at end-of-life. For Lunar probes, there are several reasons:
- The impact event at a known place and time allow other telescopes to watch, and get spectral readings on what's in the subsurface. In particular, the presence of water can be confirmed.
- Lunar orbits are unstable, and a dead probe with no maneuvering fuel left can be a hazard to other orbiting probes or end up falling on a historical site we would rather preserve. It will crash on its own eventually.
After the precedent (and disappointing results) of Prospector, you could plausibly have precision impacts planned as end-of-mission events for various probes in service at the time of the story. Especially if proper disposal becomes mandatory in a more crowded future.
So, the probe will have telemetry including video all the way down, getting very close up "before" images of the sample site. The software will be planned to have guided impact to do corrections automatically to hit the exact target, e.g. a crater wall structure.
If a future of lunar exploration includes more prospecting missions, this will be the norm. If there is also a manned presence, then targeting will be even more careful, and you will get a free excavation pit for people to follow up with visiting to see if this is a good place for mining.
The latter case might then optimize the swan song mission profile for penetration and making a deep pit, or a long trench, or whatnot.
Note that you can use the Moon's circumference and the 120-minute figure to calculate the kinetic energy. Add the kinetic energy due to the probe's altitude.