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What is the velocity of a ball falling with 100 joules of kinetic energy and a mass of 2 kilograms? Use the formula, [tex]V=\sqrt{\frac{2 K}{ m }}[/tex].

A. [tex]3 \, \text{m/s}[/tex]
B. [tex]5 \, \text{m/s}[/tex]
C. [tex]7 \, \text{m/s}[/tex]
D. [tex]8 \, \text{m/s}[/tex]
E. [tex]10 \, \text{m/s}[/tex]



Answer :

GinnyAnswer
To determine the velocity of a ball falling with 100 joules of kinetic energy and a mass of 2 kilograms, we'll use the given formula:

[tex]\[ V = \sqrt{\frac{2 K B}{m}} \][/tex]

where:
- \( V \) is the velocity,
- \( K \) is the kinetic energy,
- \( m \) is the mass.

Given values:
[tex]\[ K = 100 \text{ joules} \][/tex]
[tex]\[ m = 2 \text{ kilograms} \][/tex]

Let's substitute these values into the formula:

[tex]\[ V = \sqrt{\frac{2 \times 100}{2}} \][/tex]

Simplifying inside the square root:

[tex]\[ V = \sqrt{\frac{200}{2}} \][/tex]

[tex]\[ V = \sqrt{100} \][/tex]

[tex]\[ V = 10 \text{ m/s} \][/tex]

Therefore, the velocity of the ball is:

E. [tex]\( 10 \text{ m/s} \)[/tex]

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