AS物理学-选择题-Kinematics运动学

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201711-12-Q6

A hot-air balloon is moving vertically upwards with a constant speed of $3.00\ \mathrm{m s^{-1}}$. A sandbag is dropped from the balloon. It takes 5.00 s for the sandbag to fall to the ground.
What was the height of the balloon when the sandbag was released?
一个热气球以3.00米每秒的恒定速度垂直向上移动。沙袋从气球上掉下来。沙袋跌落到地面需要5.00秒。
释放沙袋时气球的高度是多少？

A: $29\ \mathrm{m}$

B: $108\ \mathrm{m}$

C: $123\ \mathrm{m}$

D: $138\ \mathrm{m}$

答案:

分析Analysis

Assume downward as positive direction, then initial speed is $-3.00\ \mathrm{m s^{-1}}$

假设向下为正方向，那么初始速度为 $-3.00\ \mathrm{m s^{-1}}$

constant accelerate at $g$, initial speed $u$ is given, also know $t$, thus know 3 variables out of 5 ($u$, $v$, $t$, $a$, $d$), we can use the formula $h = ut + \frac{1}{2}at^2$

匀加速运动$g$, 已知初始速度$u$, 已知$t$, 可以用5公式求出$h$

$$
h = -3 \times 5 + \frac{1}{2}g \times 5^2 = 107.625\ \mathrm{m}
$$