91Ó°ÊÓ

The given data can be listed below as,

• The mass of a pebble is, ${\mathrm{m}}_1=10\mathrm{g}$.
• The straight up distance reached by the pebble is, h = 22.0 m .
• The mass of another pebble is, ${\mathrm{m}}_2=25\mathrm{g}$.

Whenever a stone is thrown by means of a slingshot, then at the highest point of its motion, the spring energy is converted to the gravitational potential energy.

The relation to calculate the amount of potential energy stored in the slingshot’s rubber band is expressed as,

$\mathrm{U}={\mathrm{m}}_1\mathrm{gh}$

Here, is the amount of potential energy stored in the slingshot’s rubber band, is the gravitational acceleration whose value is .

Substitute all the known values in the above equation.

$$\begin{gathered} \mathrm{U}=\left(10\mathrm{g}×\frac{{10}^{-3}\mathrm{kg}}{1\mathrm{g}}\right)\left(9.81\mathrm{m}/{\mathrm{s}}^2\right)\left(22.0\mathrm{m}\right) \\ ≈2.16\mathrm{kg}.{\mathrm{m}}^2/{\mathrm{s}}^2 \\ ≈\left(2.16\mathrm{kg}.{\mathrm{m}}^2/{\mathrm{s}}^2\right)×\left(\frac{1\mathrm{J}}{1\mathrm{kg}.{\mathrm{m}}^2/{\mathrm{s}}^2}\right) \\ ≈2.16\mathrm{J} \end{gathered}$$

Thus, the amount of potential energy stored in the slingshot’s rubber band is 2.16 J .

The relation ofto calculate theheight up to which the slingshot shoot can reachis expressed as,

$$\begin{gathered} \mathrm{U}={\mathrm{m}}_2\mathrm{gh}\text{'} \\ \mathrm{h}\text{'}=\frac{\mathrm{U}}{{\mathrm{m}}_2\mathrm{g}} \end{gathered}$$

Here, h' is the height up to which the slingshot shoot can reach.

Substitute all the known values in the above equation.

$$\begin{gathered} \mathrm{h}=\left[\frac{2.16\mathrm{J}}{\left(25\mathrm{g}×{\displaystyle \frac{{10}^{-3}\mathrm{kg}}{1\mathrm{g}}}\right)\left(9.81\mathrm{m}/{\mathrm{s}}^2\right)}\right] \\ ≈8.81\mathrm{J}/\mathrm{kg}.\mathrm{m}/{\mathrm{s}}^2 \\ ≈\left(8.81\mathrm{J}/\mathrm{kg}.\mathrm{m}/{\mathrm{s}}^2\right)×\left(\frac{1\mathrm{m}}{1\mathrm{J}/\mathrm{kg}.\mathrm{m}/{\mathrm{s}}^2}\right) \\ ≈8.81\mathrm{m} \end{gathered}$$

Thus, the height up to which the slingshot shoot can reach is 8.81 m .

The physical effects that ignored in solving this problem are air resistance and no deformation of the rubber band.