Because the slide is smooth and the girl starts from rest at $A$, determine the girl's speed at $B$.
The slide is now rough. On one run the girl starts from rest at $A$ and arrives at $B$ with speed $10\,\text{m s}^{-1}$. On a different run, she is given a push from $A$ so that her initial speed is $V\,\text{m s}^{-1}$, and she reaches $B$ at $11\,\text{m s}^{-1}$. If the work done against friction is identical in both runs, determine $V$.
Because the slide is smooth and the girl starts from rest at $A$, determine her speed at $B$.
The slide is rough instead. In one case the girl begins from rest at $A$ and arrives at $B$ with speed $10\,\text{m s}^{-1}$. In another case she is launched from $A$ with initial speed $V\,\text{m s}^{-1}$ and reaches $B$ with speed $11\,\text{m s}^{-1}$. If the work done against friction is the same in both cases, find $V$.