To find the velocity of the rocket, you can use the formula for kinetic energy given by:
[tex]\[ v = \sqrt{\frac{2 \cdot KE}{m}} \][/tex]
where:
- \( KE \) is the kinetic energy, which is \( 8,000,000 \) joules.
- \( m \) is the mass of the rocket, which is \( 10,000 \) kilograms.
Step-by-step solution:
1. Substitute the given values into the formula:
[tex]\[ v = \sqrt{\frac{2 \cdot 8,000,000}{10,000}} \][/tex]
2. Multiply the kinetic energy by 2:
[tex]\[ 2 \cdot 8,000,000 = 16,000,000 \][/tex]
3. Divide the result by the mass:
[tex]\[ \frac{16,000,000}{10,000} = 1,600 \][/tex]
4. Find the square root of the result:
[tex]\[ \sqrt{1,600} = 40 \][/tex]
Therefore, the velocity of the rocket is [tex]\( 40 \)[/tex] meters per second.
