Let's consider the scenario of a soccer ball being kicked upwards into the air from a height of 3 feet. We can model the height of the soccer ball above the ground as a quadratic function using the formula $ y = -16t^2 + vt + h $, where $ v $ is the initial velocity (in feet per second) when the ball is kicked, and $ h $ is the initial height (in feet). For this example, let's assume the initial velocity of the ball is 20 feet per second. Therefore, the complete function becomes:

Question

Let's consider the scenario of a soccer ball being kicked upwards into the air from a height of 3 feet. We can model the height of the soccer ball above the ground as a quadratic function using the formula $ y = -16t^2 + vt + h $, where $ v $ is the initial velocity (in feet per second) when the ball is kicked, and $ h $ is the initial height (in feet). For this example, let's assume the initial velocity of the ball is 20 feet per second. Therefore, the complete function becomes:
$$ y = -16t^2 + 20t + 3. $$

In this function, $ y $ represents the height of the soccer ball in feet, and $ t $ is the time in seconds after the ball has been kicked. The constant value of -16 represents the acceleration due to gravity in feet per second squared (the negative sign indicates that the height decreases over time), while the initial height $ h $ of 3 feet indicates the starting position from which the ball is kicked. To predict when the ball will hit the ground, we would set $ y = 0 $ and solve for $ t $.

make this like a 6th grader wrote this

GPT-4o mini · Answer

Okay! Let’s make it simpler.

Imagine you kick a soccer ball straight up into the air from 3 feet off the ground. We can use a special math formula to see how high the ball goes. The formula looks like this:

\[ y = -16t^2 + vt + h \]

Here’s what those letters mean:

$ y $ is how high the soccer ball is above the ground (in feet).
$ t $ is the time in seconds after you kicked the ball.
$ v $ stands for the speed you kicked the ball. In this case, we kicked it at 20 feet per second.
$ h $ is the height where you kicked the ball. You kicked it from 3 feet up.

So, if we put those numbers into the formula, it becomes:

\[ y = -16t^2 + 20t + 3 \]

The number -16 is there because of gravity, which pulls the ball down. The ball starts at 3 feet high because that’s where it was kicked.

To find out when the ball will hit the ground, we want to know when $ y = 0 $ (that means it’s at ground level). So, we have to solve for $ t $ when the formula equals 0. That’s how we can figure out when the ball lands!