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A rocket with a mass of 10,000 kilograms is propelled upward with [tex]$8,000,000$[/tex] joules of kinetic energy.

What's the velocity of the rocket? Use [tex]v=\sqrt{\frac{2KE}{m}}[/tex].

The velocity of the rocket is __________ meters/second.



Answer :

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.