- Identify the distance as \(d = 18.44 \text{ m}\) and the speed as \(v = 40 \text{ m/s}\).
- Use the formula for time: \(t = \frac{d}{v}\).
- Substitute the values to find the time: \(t = \frac{18.44}{40} = 0.461 \text{ s}\).
- The ball takes \(\boxed{0.461 \text{ seconds}}\) to travel to home plate.
Explanation
- Understanding the Problem and Data Analysis
We are given that a baseball is traveling at a constant speed of \(v = 40 \text{ m/s}\). The distance from the pitcher's plate to home plate is standardly \(d = 18.44 \text{ meters}\). We need to determine the time \(t\) it takes for the ball to cover this distance. The relationship between distance, speed, and time is given by the formula \(d = v \times t\), which can be rearranged to solve for time: \[t = \frac{d}{v}.\]
- Calculating the Time
We substitute the given values into the time formula: \[t = \frac{18.44 \text{ m}}{40 \text{ m/s}}.\] By performing the division, we calculate the time in seconds: \[t = 0.461 \text{ s}.\] Thus, it takes \(0.461\) seconds for the ball to travel from the pitcher to home plate.
Examples
This calculation is a classic example of kinematics, which is essential for athletes and coaches to understand. For instance, in baseball, understanding the time it takes for a pitch to reach the plate helps hitters anticipate when to begin their swing. Similar principles apply in many other sports and everyday situations where speed, distance, and time management are critical, such as calculating the time it takes for a car to cover a certain distance at a constant speed or when coordinating timing in synchronized activities.