When in doubt, we take soundings (measure the water's depth) with the same tool Hudson's crew would have used: a lead line (or sounding line). Flags attached to the lead line mark depth in 6-foot increments (fathoms). The Half Moon has a draft of 8-1/2 feet (extending that far underwater), so it needs at least a fathom and a half of water to stay clear of the bottom.
In Hudson's day, crews would even use their lead lines to take samples of the river bottom. They could fill a small hollow on the bottom of the line's lead weight with tallow, then see what stuck to this goo when they retrieved the line. Silt or sand made for a fine anchorage, but clean tallow warned of rocks lurking below, making anchorage dangerous if not impossible.