Question
While playing catch with a friend, Brett tosses a ball into the air. Its distance above the ground in feet, f(x), depends on the number of seconds, x, since the ball left Brett's hand.
What does f(0)=f(3) tell you?
What does f(0)=f(3) tell you?
Answers
GPT-4o mini
In the context of the problem, \( f(x) \) represents the height of the ball above the ground in feet at a given time \( x \) in seconds.
The notation \( f(0) \) refers to the height of the ball at \( x = 0 \), which is the moment when Brett tosses the ball into the air. Therefore, \( f(0) \) gives you the initial height of the ball at the point of release.
The notation \( f(3) \) refers to the height of the ball at \( x = 3 \) seconds, meaning it tells you how high the ball is 3 seconds after it has been tossed.
When you see the equation \( f(0) = f(3) \), this indicates that the height of the ball at the moment it was released (0 seconds) is equal to the height of the ball 3 seconds after being tossed.
This could imply several things depending on the trajectory of the ball:
1. The ball has returned to the same height after going up and then down due to gravity.
2. The behavior could be part of a parabolic motion where the ball goes up, reaches a peak, and comes back down to the initial height at 3 seconds.
3. If there were no other forces acting on the ball (like wind resistance), it suggests that after reaching its maximum height and descending, it returns to the same height it started from, indicating symmetry in its motion.
In summary, \( f(0) = f(3) \) tells us that the height of the ball when it was thrown is the same as its height after 3 seconds, likely indicating that it has followed a parabolic path up and back down due to gravitational influence.
The notation \( f(0) \) refers to the height of the ball at \( x = 0 \), which is the moment when Brett tosses the ball into the air. Therefore, \( f(0) \) gives you the initial height of the ball at the point of release.
The notation \( f(3) \) refers to the height of the ball at \( x = 3 \) seconds, meaning it tells you how high the ball is 3 seconds after it has been tossed.
When you see the equation \( f(0) = f(3) \), this indicates that the height of the ball at the moment it was released (0 seconds) is equal to the height of the ball 3 seconds after being tossed.
This could imply several things depending on the trajectory of the ball:
1. The ball has returned to the same height after going up and then down due to gravity.
2. The behavior could be part of a parabolic motion where the ball goes up, reaches a peak, and comes back down to the initial height at 3 seconds.
3. If there were no other forces acting on the ball (like wind resistance), it suggests that after reaching its maximum height and descending, it returns to the same height it started from, indicating symmetry in its motion.
In summary, \( f(0) = f(3) \) tells us that the height of the ball when it was thrown is the same as its height after 3 seconds, likely indicating that it has followed a parabolic path up and back down due to gravitational influence.