A Pendulum and a Truck

A flatbed truck has a box of mass $M$ riding on the bed of the truck. There is a hanger on the box which supports a simple pendulum. As the truck accelerates with acceleration $A$, the box slides toward the rear of the truck but, due to friction, experiences an acceleration of $a$ in the forward direction. This causes the string of the pendulum to make an angle of $\theta$ with the vertical direction.

What is the measure of angle $\theta$ to the nearest tenth of a degree?

Details and Assumptions:

• Assume that the pendulum bob has a negligible mass of $m$.

• The coefficient of kinetic friction between the box and the truck bed is $\mu_{k}=0.5774$.