Why didn't the dove find a place to rest?
Moshav Zekenim #1, Hadar Zekenim: This was 47 days after the Ark ran aground. The tops of the mountains were exposed only after 14 more days. 1
Moshav Zekenim #2: According to Rashi, 2 we can say that the exposed mountain tops were far away.
Moshav Zekenim #3: The exposed mountain tops were muddy, and it could not sit on them.
Why did Noach have to take the dove into the Ark? It could have entered by itself!
Moshav Zekenim: He wanted to check if there was mud on its wings, to know whether or not the land had dried.