## How to manage projectile motion problems

In two-dimensional kinematics problems (for example, a ball thrown forward or a missile fired through the air), keep the horizontal ($x$) and vertical ($y$) directions separate. The motions in each direction are independent of each other, so you can work them separately.

In the $x$ direction, the velocity will be constant because there is no horizontal force on the object (ignoring air resistance). In the $y$ direction, you need to include the acceleration term due to gravity.

If the object’s initial velocity is not totally horizontal or totally vertical, you need to find the horizontal and vertical components first. If the initial velocity is $v_0$ and the initial angle is θ, then the two velocity components are:

$v_x=v_0 \cos \theta$
$v_y=v_0 \sin \theta$

Then the position functions in each direction are as follows:

$S_x=v_x t + S_{0x}$

$S_y=-\frac{1}{2}{}gt^2+v_yt+s_{0y}$

Physics
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