To find the angle θ, the horizontal distance, x needs to be known. However, the package is moving in both the x and y direction.
First, start with a diagram at the instant the package is released as shown at the left. Position the origin of the Cartesian coordinate system at the point where the package is released, with the positive y axis pointing up. Resolve the acceleration into rectangular components,
and integrate these equations over time to get velocity, and then again
to get position.
In addition to the two differential equations, initial conditions
(i.e. boundary conditions) for time, position and velocity
are needed to solve the equations. The initial conditions are:
Initial Position: xo =
0, yo = 0
Initial Velocity: vxo, =
176 ft/s, vyo = 0
Initial Time: to = 0