$(1$a$)$ The Einsteinian viewpoint that gravity is the force experienced by an object that is accelerating relative to a local inertial frame can be applied in non$-$relativistic classical mechanics also. Consider a truck that is accelerating horizontally at a uniform rate $\backslash ($ a $\backslash )$ along a level road. Relative to a local inertial frame $($a frame that is freely falling$),$ it therefore has an vertical upward component of acceleration $\backslash ($ g $\backslash )$ and a horizontal forward component of acceleration $\backslash ($ a $\backslash ).$ Calculate the magnitude and the direction of the gravitational force experienced by a mass $\backslash ($ m $\backslash )$ inside the truck.

$(1$b$)$ A helium$-$filled balloon is attached to a string inside the truck. What angle does the string make with the vertical? In which direction does the balloon tilt?