A deck chair on a ship consists of a 4 foot horizontal section for one’s legs and

A deck chair on a ship consists of a 4 foot horizontal section for one’s legs and a 3 foot vertical section for one’s back. The back section is supported by a brace to keep the angle between the two sections at 90° as shown in the top figure to the right. Length r and angle x are as shown. The brace suddenly breaks and the back section falls backwards, making both r and x larger as shown in the middle figure. Finally the back section ends up in a horizontal position as shown in the bottom figure. If angle x increases by 90° in a halfsecond at the moment the brace breaks, how fast is r changing at x= 90° (the moment that it breaks)?