BallisticsBallistics2006-07-25 16:23:332006-07-27 09:56:33Definition% this is the default PlanetPhysics preamble. as your knowledge
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Ballistics is the study of the dynamics and kinematics of a projected object.
for a start let's define a horizontal axis $x$ and a vertical axis $y$.
The Horizontal motion:
Assuming that the drag force is insignificant, the sum of forces along the $x$ axis $\Sigma F_x$ equals zero, and so the acceleration along the axis $a_x$ is also insignificant and so the velocity along the the axis $v_x$ is constant and equal to the projection velocity $V_i,x$
\[\Sigma F_x=0 \rightarrow a_x=0 \rightarrow V_x=V_i,x=V_i\cos \alpha \]
When dealing with a constant velocity motion the following kinematic function is relevant:
\[ x=x_i+v_x \cdot \Delta t \rightarrow x=x_i+ \Delta t\cdot V_i \cos \alpha \]
($x_i$-the initial position, $V_x$-the velocity aloing the axis, $\Delta t$-the duration)
The vertical motion:
The motion along the $y$ axis is under the effect of gravity $(mg)$ when $m$ is the object's mass and $g$ is the the free fall acceleration on earth. $\rightarrow \Sigma F_y=mg$
Because the force along the $y$ axis is constant the motion along the axis is evenly acclerated and so the place of the object as a function of time $y(t)$ is: \[ y= y_i+\Delta t \cdot V_i,y + 0.5g\Delta t^2 \rightarrow y= y_i+\Delta t \cdot V_i\sin\alpha + 0.5g\Delta t^2 \]