Ahorizontal metal bar oriented east-west drops straight down in a location where the earth's magnetic field is due north. as a result, an emf develops between the ends. which end is positively charged?

Metal bar is aligned along East- West direction and it is dropped vertically down

So its velocity is along -Z direction,

Now the Earth's magnetic field is towards north so its towards +Y direction

now we have formula for force on a moving charge

v = - z direction

B = + y direction

now by the above formula

So force is towards East

so all positive charge is towards East end