To find the kinetic energy of a [tex]$0.148$[/tex] kg baseball traveling at [tex]$40$[/tex] m/s, we can use the formula for kinetic energy, which is given by:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Let's break down the step-by-step solution:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = [tex]$0.148$[/tex] kg
- Velocity ([tex]\( v \)[/tex]) = [tex]$40$[/tex] m/s
2. Substitute the given values into the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} \times 0.148 \times (40)^2 \][/tex]
3. Calculate the value inside the parentheses first:
[tex]\[ (40)^2 = 1600 \][/tex]
4. Then multiply by the mass:
[tex]\[ 0.148 \times 1600 = 236.8 \][/tex]
5. Finally, multiply by [tex]$\frac{1}{2}$[/tex]:
[tex]\[ KE = \frac{1}{2} \times 236.8 = 118.4 \][/tex]
Therefore, the kinetic energy of the baseball is approximately [tex]$118.4$[/tex] Joules.
Given the options:
A. [tex]\(\frac{(0.148)(40)}{2}\)[/tex]
B. [tex]\(\frac{(0.148)(40)}{9.8}\)[/tex]
C. [tex]\(\frac{(0.148)(40)^2}{2}\)[/tex]
D. [tex]\((0.148)(40) \times 9.8\)[/tex]
The correct formula matches option C:
[tex]\[ \frac{(0.148)(40)^2}{2} \][/tex]
So, the answer is C.
