https://file.aiquickdraw.com/mathbot/file/1727405028474g9mtecbb.jpg

The image asks you to select the direction (x or y) and the equation to use in that direction. Based on the current selections in the image, you are working with the x-direction and using the equation for displacement in that direction:

\[
\Delta x = v_{0x}t + \frac{1}{2} a_x t^2
\]

This is the equation for the displacement in the x-direction under constant acceleration. You have selected the x-direction, so now you need to consider the y-direction and its corresponding equation.

### For the y-direction:
The equivalent equation is:

\[
\Delta y = v_{0y}t + \frac{1}{2} a_y t^2
\]

This equation works similarly, where:
- \(\Delta y\) is the displacement in the y-direction.
- \(v_{0y}\) is the initial velocity in the y-direction.
- \(a_y\) is the acceleration in the y-direction, which is typically gravity (i.e., \(g = 9.8 \, \text{m/s}^2\)).
- \(t\) is the time.

Would you like a further breakdown or example of how these equations are applied? 

Here are five questions to expand on this information:
1. How do you determine the initial velocity components \(v_{0x}\) and \(v_{0y}\) in projectile motion?
2. What assumptions can you make about the acceleration in the x-direction and y-direction for a projectile?
3. How does time \(t\) affect both the x and y displacements in this scenario?
4. What additional equations might be needed if you are solving for maximum height or range?
5. How does the equation for the range of a projectile relate to the horizontal displacement?

**Tip**: When analyzing motion in two dimensions, always treat the x and y directions independently unless you're working with time, which remains the same for both directions.

What direction will you start with, what are you solving for on that side, and what equation will you use?

Learn how to solve for the displacement in both the x and y directions in projectile motion using the kinematic equations Δx = v0xt + (1/2)axt^2 and Δy = v0yt + (1/2)ayt^2. This guide breaks down the steps and key concepts involved, suitable for high school students in physics.

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