To find the force exerted by the pitching machine on the baseball, we can follow these steps:
1. Identify the given values:
- Mass of the baseball, [tex]\( m = 0.15 \, \text{kg} \)[/tex]
- Initial velocity, [tex]\( u = 0 \, \text{m/s} \)[/tex]
- Final velocity, [tex]\( v = 30 \, \text{m/s} \)[/tex]
- Time, [tex]\( t = 0.5 \, \text{s} \)[/tex]
2. Calculate the acceleration:
The formula to calculate acceleration is:
[tex]\[
a = \frac{v - u}{t}
\][/tex]
Plugging in the values, we get:
[tex]\[
a = \frac{30 \, \text{m/s} - 0 \, \text{m/s}}{0.5 \, \text{s}} = \frac{30}{0.5} = 60 \, \text{m/s}^2
\][/tex]
3. Calculate the force:
The formula for force is:
[tex]\[
F = m \cdot a
\][/tex]
Using the calculated acceleration and the given mass, we obtain:
[tex]\[
F = 0.15 \, \text{kg} \cdot 60 \, \text{m/s}^2 = 9 \, \text{N}
\][/tex]
Thus, the force that the machine exerts on the baseball is [tex]\(\boxed{9}\)[/tex] newtons.
