Answer :
To determine the velocity of a ball that has a kinetic energy of 100 joules and a mass of 2 kilograms, we use the formula for kinetic energy, which is given by:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Where:
- \( KE \) is the kinetic energy in joules.
- \( m \) is the mass in kilograms.
- \( v \) is the velocity in meters per second.
We need to solve for \( v \), so we rearrange the formula to solve for \( v \).
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
[tex]\[ 2 KE = m v^2 \][/tex]
[tex]\[ v^2 = \frac{2 KE}{m} \][/tex]
[tex]\[ v = \sqrt{\frac{2 KE}{m}} \][/tex]
Now we plug in the given values:
- \( KE = 100 \) joules
- \( m = 2 \) kilograms
Substituting these values into the formula:
[tex]\[ v = \sqrt{\frac{2 \times 100}{2}} \][/tex]
[tex]\[ v = \sqrt{\frac{200}{2}} \][/tex]
[tex]\[ v = \sqrt{100} \][/tex]
[tex]\[ v = 10 \, m/s \][/tex]
Thus, the velocity of the ball is \( 10 \, m/s \).
Given the options:
A. \( 3 \, m/s \)
B. \( 5 \, m/s \)
C. \( 7 \, m/s \)
D. \( 8 \, m/s \)
E. \( 10 \, m/s \)
The correct answer is:
E. [tex]\( 10 \, m/s \)[/tex]
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Where:
- \( KE \) is the kinetic energy in joules.
- \( m \) is the mass in kilograms.
- \( v \) is the velocity in meters per second.
We need to solve for \( v \), so we rearrange the formula to solve for \( v \).
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
[tex]\[ 2 KE = m v^2 \][/tex]
[tex]\[ v^2 = \frac{2 KE}{m} \][/tex]
[tex]\[ v = \sqrt{\frac{2 KE}{m}} \][/tex]
Now we plug in the given values:
- \( KE = 100 \) joules
- \( m = 2 \) kilograms
Substituting these values into the formula:
[tex]\[ v = \sqrt{\frac{2 \times 100}{2}} \][/tex]
[tex]\[ v = \sqrt{\frac{200}{2}} \][/tex]
[tex]\[ v = \sqrt{100} \][/tex]
[tex]\[ v = 10 \, m/s \][/tex]
Thus, the velocity of the ball is \( 10 \, m/s \).
Given the options:
A. \( 3 \, m/s \)
B. \( 5 \, m/s \)
C. \( 7 \, m/s \)
D. \( 8 \, m/s \)
E. \( 10 \, m/s \)
The correct answer is:
E. [tex]\( 10 \, m/s \)[/tex]
