A car door initially at a right angle to a car will slam shut when a

car accelerates, as shown in Figure $8\mathrm{.}23.$ Assume that the door is a uniform rectangle, $1\mathrm{.}2$ m by $1\mathrm{.}2$ m square, and the acceleration is $0\mathrm{.}3$ m$/$s$2.$ Find the time required for the door to close. The problem can be solved by numerical integration or as an elliptic integral.