91影视

The given data can be listed below,

• The mass of lo is,$\mathrm{m}=8.93脳{10}^{22}\mathrm{kg}$.
• The height ejected material can gain, $h=500\mathrm{km}$.
• The radius of lo is,$r=1821\mathrm{km}$.

Moving farther away from the earth causes r to increase and the gravitational force to do negative work, causing U to increase. A body "falling" towards earth experiences a decrease in r, a positive gravitational work, and a decrease in potential.

Volcanic material can only reach to a certain height because of Io's gravity. Gravitational acceleration at Io's surface is proportional to its mass and radius.

The acceleration due to gravity at Io鈥檚 surface is given by,

$g_{\mathrm{lo}}=\frac{Gm}{R^2}$

Here, G is the gravitational constant, m is the mass of Io, and R is the radius of Io.

Substitute values in the above equation.

$$\begin{gathered} \frac{\left(6.673脳{10}^{-11}\mathrm{N}.{\mathrm{m}}^2/{\mathrm{kg}}^2\right)\left(8.93脳{10}^{23}\mathrm{kg}\right)}{{\left(1.821脳{10}^6\mathrm{m}\right)}^2} \\ =1.797\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

For constant acceleration,

$v_y^2=v_{0y}^2+2a_y\left(y-y_0\right)$ 鈥�(颈)

Here, $v_y$is the final velocity in the y-direction,$v_{0y}$is the initial velocity inthe y-direction, $a_y$is the acceleration in the y-direction, y is the final point in y direction,$y_0$is the initial point.

When , $v_y=0$theabove equation becomes,

$v_{0y}=\sqrt{-a_y\left(y-y_0\right)}$

Substitute values in the above,

$$\begin{gathered} v_{0y}=\sqrt{-2\left(-1.797m/s^2\right)\left(5.00脳{10}^{5}m\right)} \\ =1.3405脳{10}^{3}m/s \end{gathered}$$

By using equation (i),

$y-y_0=\frac{v_y^2-v_{0y}^2}{2a_y}$

Substitute values in the above,

$$\begin{gathered} \mathrm{y}-{\mathrm{y}}_0=\frac{-\left(1.3405脳{10}^3\mathrm{m}/\mathrm{s}\right)}{2\left(-9.80\mathrm{m}/{\mathrm{s}}^2\right)} \\ =9.17脳{10}^3\mathrm{m}\left(\frac{1\mathrm{km}}{100\mathrm{m}}\right) \\ =9.17\mathrm{km} \end{gathered}$$

Thus, when the material is ejected at the same speed as Io on earth, it will go up to 91.7 km .