a baseball player hits a fly ball that is caught about 5 seconds later by an outfielder. the path of the ball is a parabola. the ball is at its highest point as it passes the second baseman, who is 117 feet from home plate. about how far from home plate is the out fielder at the moment he catches the ball? explain your reasoning.
The highest point, the vertex is halfway out because the parabola is symmetric about vertical line through the vertex.
so at 117*2 = 234.
To find the distance from home plate to the outfielder when he catches the ball, we need to consider the path of the ball as a parabolic curve and use the given information.
Let's break down the problem step by step:
1. We know that the ball takes 5 seconds to be caught by the outfielder. Since the ball is at its highest point when it passes the second baseman, we assume that the total time taken by the ball in the air is symmetrical. Therefore, the ball reaches its highest point after 5/2 = 2.5 seconds.
2. Now, let's find the horizontal distance covered by the ball in 2.5 seconds. Since the ball has traveled half of its total time, the horizontal distance covered is half of the total distance covered horizontally.
3. We are given that the second baseman is 117 feet away from home plate. Since the path of the ball is a parabolic curve, the horizontal distance covered by the ball in 2.5 seconds is also the horizontal distance between the outfielder and home plate when the ball is caught.
Hence, the outfielder is approximately 117 feet away from home plate when he catches the ball.
To find the distance from home plate to the outfielder when he catches the ball, we need to use the information provided.
First, let's break down the problem:
1. The ball follows a parabolic path.
2. The ball reaches its highest point as it passes the second baseman, who is 117 feet from home plate.
Based on these details, we can assume that the path of the ball is symmetrical. Therefore, the highest point is located in the middle between the second baseman and the outfielder. Let's call this point "X."
To find the distance from home plate to the outfielder, we need to find the distance from home plate to "X" and then double it.
Since the second baseman is 117 feet from home plate, the distance from home plate to point "X" is half of this distance, which is 117/2 = 58.5 feet.
Now, to find the total distance from home plate to the outfielder, we double this value: 58.5 * 2 = 117 feet.
Therefore, the outfielder is approximately 117 feet from home plate at the moment he catches the ball.
Note: This is an approximation since the exact location of the highest point of the ball's trajectory is unknown.