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### 307-Z: Memorize Kinematic Equations 3

• Topic Cluster: Kinematics
• Topic: Projectile Motion
• Objective: Memorize the Kinematic Equations as they apply to two dimensional motion and projectile motion.
• Content: The four kinematic equations and constant velocity motion can be applied to each dimension; in projectil emotion a particle undergoes constant velocity motion in the horizontal and accelerated motion in the vertical dimension.
• Level: 3

#### BACK to Ladder Projectile Motion

Memorize the equations below, which represent kinematic equations in each dimension:

### Vertical Dimension

#### Constant Velocity Motion

• $$\Delta x = v_x \cdot \Delta t$$
• $$\Delta y = v_y \cdot \Delta t$$

#### Accelerated Motion

• $$v_{fx} = v_{ix} + a_x \cdot \Delta t$$
• $$\Delta x = v_{ix} \cdot \Delta t + \frac{1}{2} a_x \left( \Delta t \right)^2$$
• $$\Delta x = \left( \frac{v_{ix} + v_{fx}}{2} \right) \Delta t$$
• $$v_{fx}^2 = v_{ix}^2 + 2 a_x \cdot \Delta x$$
• $$v_{fy} = v_{iy} + a_y \cdot \Delta t$$
• $$\Delta y = v_{iy} \cdot \Delta t + \frac{1}{2} a_y \left( \Delta t \right)^2$$
• $$\Delta y = \left( \frac{v_{iy} + v_{fy}}{2} \right) \Delta t$$
• $$v_{fy}^2 = v_{iy}^2 + 2 a_y \cdot \Delta y$$

In a typical cannon problem: you would use the constant velocity equation in the horizontal dimension amd the accelerated motion equations in the vertical dimension.

In the table below, the same equations are presented but those that are relevant to a cannon problem are circled:

### Vertical Dimension

#### Constant Velocity Motion

• $$\Delta x = v_x \cdot \Delta t$$
• $$\Delta y = v_y \cdot \Delta t$$

#### Accelerated Motion

• $$v_{fx} = v_{ix} + a_x \cdot \Delta t$$
• $$\Delta x = v_{ix} \cdot \Delta t + \frac{1}{2} a_x \left( \Delta t \right)^2$$
• $$\Delta x = \left( \frac{v_{ix} + v_{fx}}{2} \right) \Delta t$$
• $$v_{fx}^2 = v_{ix}^2 + 2 a_x \cdot \Delta x$$
• $$v_{fy} = v_{iy} + a_y \cdot \Delta t$$
• $$\Delta y = v_{iy} \cdot \Delta t + \frac{1}{2} a_y \left( \Delta t \right)^2$$
• $$\Delta y = \left( \frac{v_{iy} + v_{fy}}{2} \right) \Delta t$$
• $$v_{fy}^2 = v_{iy}^2 + 2 a_y \cdot \Delta y$$