一个质量为 $1.6\,\mathrm{kg}$ 的质点从水平地面上方 $9\,\mathrm{m}$ 高处由静止释放。质点撞击地面前瞬间的速率为 $12\,\mathrm{m\,s^{-1}}$。

求克服空气阻力所做的功。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

Where a numerical value for the acceleration due to gravity ($g$) is needed, use $10\,\mathrm{m\,s^{-2}}$.

需要使用重力加速度 $g$ 的数值时，取 $10\,\mathrm{m\,s^{-2}}$。

空气阻力不必恒定，用初始势能减落地动能，直接求克服阻力的总功。

The loss of gravitational potential energy is $1.6(10)(9)=144\,\mathrm{J}$, and the final kinetic energy is $\tfrac12(1.6)(12^2)=115.2\,\mathrm{J}$. Hence the work done against air resistance is