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307-Z: Memorize Kinematic Equations 3

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307-Z: Memorize Kinematic Equations 3

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

Horizontal Dimension

Vertical Dimension

Constant Velocity Motion

Constant Velocity Motion

  • \( \Delta x = v_x \cdot \Delta t \)
  • \( \Delta y = v_y \cdot \Delta t \)

Accelerated Motion

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:

Horizontal Dimension

Vertical Dimension

Constant Velocity Motion

Constant Velocity Motion

  • \( \Delta x = v_x \cdot \Delta t \)
  • \( \Delta y = v_y \cdot \Delta t \)

Accelerated Motion

Accelerated Motion

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

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