Problem Diagram

Skew View

Top View

Side View

Begin with a diagram at the instant the arm is perpendicular to the path of the truck:

Place the origin (Point A) of the translating coordinate axes xyz at the base of the arm, with the positive x axis parallel to the path of the truck.

The stationary XYZ axes are fixed to the ground.

Using the right-hand rule, we can express the angular velocity and acceleration about the vertical axis as

     ω_z = -0.2k rad/s

     α_z = -0.8k rad/s²

Similarly, the angular velocity about the horizontal axis can be expressed as

     ω_x = -0.1k rad/s

The position of the top of the arm (Point B) in the translating system is described by

     r_B/A = 40 cos30j + 40 sin30k

The velocity of point B is given by

     v_B = v_A + ω × r_B/A

     v_B = 41.93i + 2.00j - 3.46k  ft/s

The acceleration of point B can be found from

     a_B = a_A + α × r_B/A + ω × ( ω × r_B/A)

     a_B = 28.12i - 8.73j - 0.2k  ft/s²