A simple accelerometer can be made by suspending a small massive object from a string attached to a fixed point on an accelerating object. Suppose such an accelerometer is attached to point P on the ceiling of an automobile traveling in a straight line on a flat surface at constant acceleration. Due to the acceleration, the string will make an angle θ with the vertical.
(a) Show that the magnitude of the acceleration a is related to the angle θ by a = gtanθ. (Do this on paper. Your instructor may ask you to turn in this work.)
(b) Suppose the automobile brakes steadily to rest from 45 km/h over a distance of 57 m. What angle will the string make with the vertical?