A ball is initially rolling on a flat ground, then, it climbs up a wall as shown in the diagram.
Consider two cases,
1) The wall is rough enough that the ball rolls through out the climb.
2) The wall is smooth.
In which case did the ball will climb to a greater height?
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The ball can only go up a wall if it has an early enough start, particularly rolled down from the opposite wall or someone threw it. And, even in those 2 cases, it needs a rough enough wall to give good traction. A smooth wall… it could never go up that at all.