- cause or allow to sink to a lower position
- let or make to fall vertically
When I say “I dropped the baton” without further information like “to the floor,” can the listeners interpret it as "the baton went down off my hand"?
I agree with J.R.'s comment but would like to add that sometimes it matters where what you dropped landed. If you dropped your Kindle, as Noah suggests, it matters whether you dropped it onto the floor or onto your bed. I dropped my Kindle last month and it broke because it hit the floor and not my bed. I wouldn't qualify I dropped the baton by saying where it landed unless that information made a difference. I dropped the ball is an idiom that has nothing to do with where the ball falls, but has everything to do with your failure. If context tells the listeners where the dropped object was dropped, it's not necessary to say where it landed, only, perhaps, what happened to it. But if that doesn't matter, saying that you dropped it is enough to let the listeners know that it escaped your grasp and fell downward.
“I dropped the baton” without further information means exactly that and makes complete sense by itself.
'Any further information' becomes necessary to be included when such information is relevant and significant to the context.
In a hypothetical situation, you could be dropping it somewhere mid-way between the Earth and the Moon. There's no telling if it "falls" to the "ground" or "floats" to the lunar surface. You may have to tell.
On the other hand,
I both disagree and agree with many of these answers. While adding information will always make more things clear to people, in almost all situations, it is not necessary in these cases. It is perfectly legitimate to say "I dropped my Kindle." even though the material on which it lands makes a difference to the object based on its physical composition, that information is not required. Just as if you said "I talked to Jan." as opposed to " I talked to Jan about her attempted suicide." It makes a big difference but is not necessary.
In essence with the use of the verb "to drop," people will know that the object moved to a lower position as a cause of, gravity. They may not know If your Kindle is ok, but they will know the position change of the object just as your dictionary definition's stated.
Someone might say: "I dropped my Kindle but it wasn't damaged." Someone also might say: "I dropped my Kindle, now I have to order a new one online." Both of these sentences use the verb "to drop" just fine and are grammatically correct.