Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

A girl with mass $40\,\text{kg}$ moves down a slide in a water park. She begins at point $A$ and travels to point $B$, which lies $7.2\,\text{m}$ vertically beneath the level of $A$, as the diagram shows.
(a(i))[2]

Because the slide is smooth and the girl starts from rest at $A$, determine the girl's speed at $B$.

(a(ii))[3]

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 $V$.

(i)[2]

Because the slide is smooth and the girl starts from rest at $A$, determine her speed at $B$.

(ii)[3]

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 $V$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Energy equation used: $\tfrac12 \times 40 \times v^2 = 40 \times g \times 7.2$

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