Question

If a Saturn V rocket with an Apollo spacecraft attached had a combined mass of $\mathbf{2}\mathbf{.}\mathbf{9}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}\mathbf{}\mathbf{kg}$and reached a speed of $\mathbf{11}\mathbf{.}\mathbf{2}\mathbf{}\mathbf{km}\mathbf{/}\mathbf{s}$, how much kinetic energy would it then have?

Short answer

The kinetic energy of a Saturn V rocket with an attached Apollo spacecraft is $1.81\times {10}^{13}\mathrm{J}$.

Step-by-step solution

Given data

1. The combined mass of the Saturn V rocket and the spacecraft, $\mathrm{m}=2.9\times {10}^5\mathrm{kg}$.
2. Speed, $\mathrm{v}=11.2\mathrm{km}/\mathrm{s}=11200\mathrm{m}/\mathrm{s}$.

Understanding the concept

Using the formula of kinetic energy and fromthegiven mass and speed, we can find the kinetic energy of a Saturn V rocket with an attached Apollo spacecraft.

Formula:

$\mathrm{KE}=\frac{1}{2}{\mathrm{mv}}^2$

Calculate the kinetic energy the rocket would have had

The kinetic energy can be calculated using the formula as,

$\mathrm{KE}=\frac{1}{2}{\mathrm{mv}}^2$

Substitute the values in the above formula, and we get,

$$\begin{gathered} \mathrm{KE}=\frac{1}{2}\left(2.9\times {10}^5\mathrm{kg}\right){\left(11200\frac{\mathrm{m}}{\mathrm{s}}\right)}^2 \\ \mathrm{KE}=1.81\times {10}^{13}\mathrm{J} \end{gathered}$$

Therefore, the kinetic energy of a Saturn V rocket with an attached Apollo spacecraft is $1.81\times {10}^{13}\mathrm{J}$.