To determine the force exerted by the pitching machine on the baseball, follow these steps:
1. Identify the given values:
- Initial velocity ([tex]\(u\)[/tex]): 0 meters/second
- Final velocity ([tex]\(v\)[/tex]): 30 meters/second
- Time ([tex]\(t\)[/tex]): 0.5 seconds
- Mass ([tex]\(m\)[/tex]): 0.15 kilograms
2. Calculate the acceleration ([tex]\(a\)[/tex]):
- The formula for acceleration is given by:
[tex]\[ a = \frac{v - u}{t} \][/tex]
- Substitute the values into the formula:
[tex]\[ a = \frac{30 \, \text{m/s} - 0 \, \text{m/s}}{0.5 \, \text{s}} \][/tex]
- Calculate the acceleration:
[tex]\[ a = \frac{30}{0.5} = 60 \, \text{m/s}^2 \][/tex]
3. Calculate the force ([tex]\(F\)[/tex]):
- The formula for force is given by:
[tex]\[ F = m \cdot a \][/tex]
- Substitute the values into the formula:
[tex]\[ F = 0.15 \, \text{kg} \times 60 \, \text{m/s}^2 \][/tex]
- Calculate the force:
[tex]\[ F = 9 \, \text{N} \][/tex]
Therefore, the force the pitching machine exerts on the baseball is [tex]\(9\)[/tex] newtons.
