Question

Is a baseball and cannon are dropped from the same height at the same time, which ball will hit the ground first?

Answer 1

If you include the effects of falling through air, then you have to know the
shape, size, weight, and surface texture of the objects.  You also have to
know the height from which they're dropped, and the temperature, pressure,
and humidity of the air.  All these things make a difference in how they fall.

If you ignore the effects of falling through air, like build a giant metal tank
and pump all the air out of it, and ONLY talk about the effects of gravity, then
ALL OBJECTS accelerate at the same rate.  If you drop two things from the
same height at the same time, then they both hit the ground at the same time,
traveling at the same speed, no matter what they are.  They could be a piece of
tissue and a car ! 

There are several museums where they have a big glass pipe that you can
see through, and they pump the air out of the pipe and drop a feather and a
bowling ball from the top inside at the same time, and they both reach the
bottom together.   

If gravity is the only force on an object, then all objects fall at the same rate.

Answer 2

Depends on the height. If they are dropped at a height which is high enough for them to reach terminal velocity, they will hit the ground at the same time. However, if they are dropped from a lower height, say, an average rooftop, the cannon will hit the ground first because it has the greater mass