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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{2KE}{m}} [/tex].

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

Sagot :

GinnyAnsweridn
To find the velocity of a ball given its kinetic energy and mass, we use the formula:

[tex]\[ V = \sqrt{\frac{2 \cdot KE}{m}} \][/tex]

where:
- [tex]\( KE \)[/tex] is the kinetic energy
- [tex]\( m \)[/tex] is the mass

In this problem:
- [tex]\( KE = 100 \, \text{joules} \)[/tex]
- [tex]\( m = 2 \, \text{kilograms} \)[/tex]

Now, let's substitute the given values into the formula:

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

Simplify the expression inside the square root:

[tex]\[ \frac{2 \cdot 100}{2} = \frac{200}{2} = 100 \][/tex]

So, we have:

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

Taking the square root of 100:

[tex]\[ V = 10 \][/tex]

Therefore, the velocity of the ball is:

[tex]\[ 10 \, \text{m/s} \][/tex]

The correct answer is:

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