Final answer:
Velocity components in the Earth axis system are found by using vector addition and then transformed back into the body axis system through a coordinate transformation. Angular velocity and gravitational force are also considered, with gravitational acceleration assumed as -9.80 m/s². Kinematic equations are employed to solve for unknown quantities.
Step-by-step explanation:
To find velocity components in the Earth axis system, one must decompose the velocity vector into its x and y component vectors, where the x-axis and y-axis are defined with respect to the Earth. This can be done using vector addition if the initial velocities in perpendicular directions are known. Then, to transform back into the body axis system, one would apply a coordinate transformation using rotational matrices that relate the Earth axis system to the body axis system. This transformation takes into account the orientation of the body in relation to the Earth-fixed reference frame.
Regarding the rotational aspects, it's important to consider angular velocity, which is represented by a vector pointing along the axis of rotation, determined by the right-hand rule. When considering motion, the only force we are assuming is gravitational force, where the acceleration component is ay = -g or -9.80 m/s2 when taking the upward direction as positive.
Finally, to solve for initial velocity or other unknowns, a suitable kinematic equation should be used that relates displacement, velocity, acceleration, and time. This equation, in coordination with the principles of vector addition and the nature of centrifugal acceleration, will allow us to find the total displacement and velocity vectors.