Whether wave or ledge, you're facing the uncomfortable prospect of a hard landing.
What's your best solution? In many cases, simply shorten your boat.
Now, no one is suggesting that you clamber out on your foredeck while sliding down the river, but there's a simple technique that will give you all the advantages of a shorter boat without dramatic hacking and cutting.
First, a look at the scenario. You're riding a current and you're coming up on an abrupt change in water level. To repeat, you might be drifting down on a ledge in the river, riding a series of rollers in deep water on the ocean or lake, or riding a wave into the beach. If you head directly down current, your bow will first extend out over the change in levels, and as more and more of your boat follows, you'll follow an arc much like a javelin. And just like the point of a javelin, you're going to plant your bow into whatever is at the bottom of the drop. When running a ledge, that's the bottom of the river. When surfing in toward shore, that's the unforgiving beach. In an ocean roller, that's the slower energy flow in the trough of the wave. In each scenario, you're facing a violent broach as your bow stops and the full energy of the water pushes your stern. If you don't break your bow in the bottom, you're going to rotate like a piece of underdone meat on a rotisserie. This is not fun.
So how do you shorten your boat? Simple, turn it at an angle to the current. Think of your boat's effective length not as the distance from bow to stern but instead as its relative length from the most downstream point to the most upstream point. At the ridiculous extreme, if you swing your boat at right angles to the current, its relative length is the distance from the downstream gunwale to the upstream gunwale, or only about 26 inches.
By angling your boat to the current as you approach the lip of the ledge, you eliminate much of the "javelin arc" and instead of spearing the bottom of the ledge you'll land much flatter and more on the bottom of the hull.
For the cruising kayaker, instead of dropping directly down the face of the wave, you angle across the face of the wave - keeping your bow higher and missing either the counter current in the trough of a deep-water wave or the beach itself at the foot of slumping surf.
There's a second advantage for the aggressive river paddler. If there is a steep, grabby hole at the bottom of a drop, angling your boat presents a shorter boat to the hole and will aid in keeping the hole from grabbing your stern. A violent rear-endo can be a thing of beauty, if that's what you want to do, but an inadvertent one can yank every bit of control out of your line down the rapid. If you're trying to skip over a grabby hole, hit the top of the drop with serious speed in order to clear the recirculation.