how fast do you need to swing a 100g ball at the end of a string in a horizontal circle of 60 cm radius so that the string makes a 28 degree angle relative to the horizontal

90°

Explanation:

This angle is the measured between the force applied and the displacement where the force vector and the displacement vector are on opposite direction.

The formula for work in this case is ;

W=F*d* cos ∅ where ;

F= force, d= distance and ∅ is the work angle

For minimum work ∅ =  90°

For maximum work ∅ = 0°