Question
Lucas threw a ball up into the air from a
height of how many feet? The ball reached a
maximum height of 13 feet when it was
a horizontal distance of 4.5 feet from
Lucas. The ball landed on the ground how many
feet from Lucas.?
height of how many feet? The ball reached a
maximum height of 13 feet when it was
a horizontal distance of 4.5 feet from
Lucas. The ball landed on the ground how many
feet from Lucas.?
Answers
GPT-4o mini
To determine how far the ball landed from Lucas, we can analyze the situation using the properties of a parabola. The ball's trajectory can be modeled as a parabola, and the point it reaches the maximum height forms the vertex of this parabola.
We know the following:
- The maximum height reached by the ball is 13 feet (vertex of the parabola).
- The horizontal distance from Lucas when the ball reaches the maximum height is 4.5 feet.
Since the parabola is symmetric about its vertex, we can deduce that the ball will land at an equal distance away from Lucas on the other side of the vertex. Therefore, if the maximum height is reached at 4.5 feet away, it will land an equal distance away on the other side, which would also be 4.5 feet.
Thus, the total distance from Lucas when the ball lands is:
\[
4.5 \, \text{feet} + 4.5 \, \text{feet} = 9 \, \text{feet}.
\]
So, the ball landed **9 feet** from Lucas.
We know the following:
- The maximum height reached by the ball is 13 feet (vertex of the parabola).
- The horizontal distance from Lucas when the ball reaches the maximum height is 4.5 feet.
Since the parabola is symmetric about its vertex, we can deduce that the ball will land at an equal distance away from Lucas on the other side of the vertex. Therefore, if the maximum height is reached at 4.5 feet away, it will land an equal distance away on the other side, which would also be 4.5 feet.
Thus, the total distance from Lucas when the ball lands is:
\[
4.5 \, \text{feet} + 4.5 \, \text{feet} = 9 \, \text{feet}.
\]
So, the ball landed **9 feet** from Lucas.