Question

A model rocket with a mass of 1.4kg is launched straight up at a speed of 43m/s.
4. What is its potential energy at the maximum height? 5. What is the rocket's maximum height? 6. What is the rocket's speed at a height of 47.17m?

Answer 1

A model rocket with a mass of $1.4\mathrm{kg}$ is launched straight up at a speed of $43\mathrm{m/s}$.

4. What is its potential energy at the maximum height? 5. What is the rocket's maximum height?

6. What is the rocket's speed at a height of $47.17\mathrm{m}$?

Solution:

Let:

$$m = 1.4 \, \mathrm{kg}$$ $$v_0 = 43 \, \mathrm{m/s}$$ $$h = 47.17 \, \mathrm{m}$$ $$E_p - ?$$ $$H - ?$$ $$v_h - ?$$

$E_p = mgH$, where $g = 9.8 \, \mathrm{m/s^2}$ gravitational acceleration

$$H = \frac{1}{2} g t^2, \, v = g t \Rightarrow t = \frac{v}{g}$$ $$H = \frac{v^2}{2g}$$ $$H = \frac{43^2}{2 \cdot 9.8} = 94.34 \, \mathrm{m}$$ $$E_p = 1.4 \cdot 9.8 \cdot 94.34 = 1294.35 \, \mathrm{J}$$ $$v = v_0 - g t, \, t = \sqrt{\frac{2h}{g}} \Rightarrow$$ $$v = v_0 - \sqrt{2 g h}$$ $$v_h = 43 - \sqrt{2 \cdot 9.8 \cdot 47.17} = 12.6 \, \mathrm{m/s}$$

Answer: $E_p = 1294.35 \, \mathrm{J}$, $H = 94.34 \, \mathrm{m}$, $v_h = 12.6 \, \mathrm{m/s}$.