A small sphere is hung by a string from the ceiling of a van. When the van is stationary, the sphere hangs vertically. However, when the van accelerates, the sphere swings backward so that the string makes an angle of ( with respect to the vertical.
(a) Derive an expression for the magnitude a of the acceleration of the van in terms of the angle u and the magnitude g of the acceleration due to gravity.
(b) Find the acceleration of the van when ( = 10.0o.
(c) What is the angle ( when the van moves with a constant velocity?