what is the magnitude of its velocity just before it strikes the ground, if the bottle was thrown straight out horizontally from the tower with a speed of 11.8 m/s?

Answer :

There's not enough given information to find the answer.

The horizontal velocity has no effect on anything that happens vertically. To find the object's vertical speed when it hits the ground, we need to know what height it was dropped from, and that's not given in the question.