**Problem Statement:** An object is dropped from a height of 22 meters. Ignoring air resistance, how long until the object hits the ground? What is the object's final velocity right before impact? **Given Information:** - Displacement (\(\Delta x\)) = -22 m - Acceleration (\(a\)) = -9.8 m/s² (due to gravity) - Initial velocity (\(v_i\)) = 0 m/s - Final velocity (\(v_f\)) and time (\(t\)) are unknown and need to be determined. **Formulas:** 1. **Equation of Motion for Displacement:** \[ x = \frac{1}{2} a t^2 \] 2. **Equation for Final Velocity:** \[ v_f = at \] 3. **Equations for Acceleration and Velocity (not directly used here):** \[ a = \frac{(v_f - v_i)}{t} \] \[ v_f^2 = v_i^2 + 2ax \] \[ x = \left(\frac{v_i + v_f}{2}\right)t \] **Explanation of Diagram:** The diagram outlines the approach to solve the problem using the equations of motion. It sets the initial conditions and shows step-by-step how to find the time of flight and final velocity without solving the equations explicitly in this image. The goal is to rearrange and solve these formulas to find the time \(t\) and the final velocity \(v_f\) when the object hits the ground. Certainly! Below are the transcribed kinematic equations from the image, which are fundamental for describing motion in physics: ### Kinematic Equations 1. **Acceleration (a):** \[ a = \frac{(v_f - v_i)}{t} \] This formula calculates acceleration as the change in velocity (\(v_f - v_i\)) over time (\(t\)). 2. **Displacement (x) with Initial Velocity and Acceleration:** \[ x = v_i t + \frac{1}{2} a t^2 \] This equation gives the displacement (\(x\)) of an object, factoring in its initial velocity (\(v_i\)), time (\(t\)), and acceleration (\(a\)). 3. **Final Velocity (v_f):** \[ v_f = v_i + at \] This equation calculates the final velocity (\(v_f\)) of an object, considering its initial velocity (\(v_i\)) and acceleration (\(a\)) over time (\(t\)). 4. **Final Velocity Squared:** \[ v_f^2 = v_i^2 + 2ax \] This formula relates the square of the final velocity (\(v_f^2\)) to the square of the initial velocity (\(v_i^2\)), acceleration (\(a\)), and displacement (\(x\)). 5. **Displacement (x) with Average Velocity:** \[ x = \left( \frac{v_i + v_f}{2} \right) t \] This equation calculates the displacement using the average of the initial (\(v_i\)) and final velocities (\(v_f\)), over time (\(t\)). These equations are essential for analyzing linear motion in one dimension in physics.

Problem Statement: An object is dropped from a height of 22 meters. Ignoring air resistance, how long until the object hits the ground? What is the object's final velocity right before impact? Given Information: - Displacement (\(\Delta x\)) = -22 m - Acceleration (\(a\)) = -9.8 m/s² (due to gravity) - Initial velocity (\(v_i\)) = 0 m/s - Final velocity (\(v_f\)) and time (\(t\)) are unknown and need to be determined. Formulas: 1. Equation of Motion for Displacement: \[ x = \frac{1}{2} a t^2 \] 2. Equation for Final Velocity: \[ v_f = at \] 3. Equations for Acceleration and Velocity (not directly used here): \[ a = \frac{(v_f - v_i)}{t} \] \[ v_f^2 = v_i^2 + 2ax \] \[ x = \left(\frac{v_i + v_f}{2}\right)t \] Explanation of Diagram: The diagram outlines the approach to solve the problem using the equations of motion. It sets the initial conditions and shows step-by-step how to find the time of flight and final velocity without solving the equations explicitly in this image. The goal is to rearrange and solve these formulas to find the time \(t\) and the final velocity \(v_f\) when the object hits the ground. Certainly! Below are the transcribed kinematic equations from the image, which are fundamental for describing motion in physics: ### Kinematic Equations 1. Acceleration (a): \[ a = \frac{(v_f - v_i)}{t} \] This formula calculates acceleration as the change in velocity (\(v_f - v_i\)) over time (\(t\)). 2. Displacement (x) with Initial Velocity and Acceleration: \[ x = v_i t + \frac{1}{2} a t^2 \] This equation gives the displacement (\(x\)) of an object, factoring in its initial velocity (\(v_i\)), time (\(t\)), and acceleration (\(a\)). 3. Final Velocity (v_f): \[ v_f = v_i + at \] This equation calculates the final velocity (\(v_f\)) of an object, considering its initial velocity (\(v_i\)) and acceleration (\(a\)) over time (\(t\)). 4. Final Velocity Squared: \[ v_f^2 = v_i^2 + 2ax \] This formula relates the square of the final velocity (\(v_f^2\)) to the square of the initial velocity (\(v_i^2\)), acceleration (\(a\)), and displacement (\(x\)). 5. Displacement (x) with Average Velocity: \[ x = \left( \frac{v_i + v_f}{2} \right) t \] This equation calculates the displacement using the average of the initial (\(v_i\)) and final velocities (\(v_f\)), over time (\(t\)). These equations are essential for analyzing linear motion in one dimension in physics.