To determine the acceleration of the baseball when it is thrown straight down and is experiencing a drag force, we can use Newton's second law of motion, which states that:
\[ F_{net} = m \cdot a \]
where \( F_{net} \) is the net force acting on the object, \( m \) is the mass of the object, and \( a \) is its acceleration.
The forces acting on the baseball are the gravitational force (weight) and the drag force. The gravitational force can be calculated using:
\[ F_{gravity} = m \cdot g \]
where \( g \) is the acceleration due to gravity, approximately \( 9.81 , \text{m/s}^2 \).
- Calculate the gravitational force acting on the baseball:
\[ F_{gravity} = 0.145 , \text{kg} \cdot 9.81 , \text{m/s}^2 = 1.42145 , \text{N} \]
- The drag force is acting upwards and is given as \( 0.4 , \text{N} \). Therefore, we can express the net force as:
\[ F_{net} = F_{gravity} - F_{drag} \]
Substituting in the values we found:
\[ F_{net} = 1.42145 , \text{N} - 0.4 , \text{N} = 1.02145 , \text{N} \]
- Now use Newton's second law to find the acceleration:
\[ F_{net} = m \cdot a \]
\[ a = \frac{F_{net}}{m} = \frac{1.02145 , \text{N}}{0.145 , \text{kg}} \approx 7.04 , \text{m/s}^2 \]
Thus, the acceleration of the baseball at that speed is approximately \( 7.04 , \text{m/s}^2 \) downward.