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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 \, \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]

Sagot :

GinnyAnswer
To find the velocity of the ball, we'll use the given formula for velocity in terms of kinetic energy and mass:
[tex]\[ V = \sqrt{\frac{2KE}{m}} \][/tex]

Here's a step-by-step breakdown of the solution:

1. Identify the given values:
- Kinetic Energy (\(KE\)) = 100 Joules
- Mass (\(m\)) = 2 kilograms

2. Substitute these values into the formula:
[tex]\[ V = \sqrt{\frac{2 \times 100}{2}} \][/tex]

3. Simplify the expression under the square root:
[tex]\[ V = \sqrt{\frac{200}{2}} \][/tex]
[tex]\[ V = \sqrt{100} \][/tex]

4. Take the square root of 100:
[tex]\[ V = 10 \][/tex]

Therefore, the velocity \( V \) is 10 meters per second.

The correct answer is:
[tex]\[ \boxed{10 \, m/s} \][/tex]
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