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