A simple accelerometer can be made by suspending a small object from a string attached to a fixed point on an accelerating object---to the ceiling of a passenger car, for example. When there is an acceleration, the object will deflect and the string will make some angle with the vertical.

(a) How is the direction in which the suspended object deflects related to the direction of the acceleration? 

(b) Show that the acceleration a is related to the angle θ that the string makes by a = g tan θ; 

(c) Suppose the accelerometer is attached to the ceiling of an automobile that brakes to rest from 50 km/h in a distance of 60 m. What angle will the accelerometer make? Will the object swing forward or backward?