Question

A jet is travelling at a speed of 1200 km/h and drops cargo from a height of 25 km above the ground. Calculate the time it takes for the cargo to hit the ground and the range it travels

Answer 1

Question#22883

A jet is travelling at a speed of $1200\,\mathrm{km/h}$ and drops cargo from a height of $25\,\mathrm{km}$ above the ground. Calculate the time it takes for the cargo to hit the ground and the range it travels

Solution:

Let:

$$v = 1200\,\mathrm{km/h} = 333.33\,\mathrm{m/sec}$$ $$H = 25\,\mathrm{km} = 25000\,\mathrm{m}$$ $$t = ?, S = ?$$ $$S = vt$$

Such as cargo freely falls from height $H$:

$$t = \sqrt{\frac{2H}{g}}, \text{ where } g \text{ is the acceleration due the gravitation}.$$ $$t = \sqrt{\frac{2 \cdot 25000}{9.8}} = 71.4\,\mathrm{sec}$$ $$S = 333.33 \cdot 71.4 = 23800\,\mathrm{m}$$

Answer: the time is 71.4 sec., the traveling distance is $23800\,\mathrm{m}$.