Does a thicker core make the electromagnet stronger?

Yes

Explanation:

The core of an electromagnet serves to stabilize the magnetic field created by the wire. The thicker the core, the more metal there is to amplify the current. Therefore, a thicker core does make an electromagnet stronger. Hope this helps!

Yes

Explanation:

The bigger the core the stronger the magnetic field that is produced. This because a wider surface area is produced through which the magnetic field can be felt.

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be