Question

as the sun began to set, the island castaway was barely able to discern a ship on the horizon. did that mean that someone onboard the ship might be able to notice him, too? he jumped to his feet and frantically waved his arms, yelling, \over here! over here!\
to reach

to detect

to search for

Explanation:

To solve this, we analyze the meaning of "discern" in the context. "Discern" here means to be able to see or detect something (the ship on the horizon). "To reach" means to get to a place, which doesn't fit. "To search for" means to look for something actively, but the castaway is just seeing the ship, not searching. "To detect" means to notice or find, which matches the meaning of "discern" in this sentence.

Answer:

to detect