Christmas Math Problem 2

In Santa's workshop, there is a large, rectangular room. All of the points on this rectangle are labelled $A$ , $B$ , $C$ , and $D$ . $A$ and $B$ are the two points on the corners on the floor, and $C$ and $D$ are the ones on the roof. We are going to assume that this room is two-dimensional, so there are only four points. Inside of this rectangular room, there is a skating rink across the floor, which is used by all of the elves in Santa's workshop. This skating rink stretches all the way from point $A$ to point $B$ , across the floor. Above this skating rink is a slide, and a ramp leading up to the slide. This slide and ramp stretch all the way over the skating rink, ending at the points $A$ and $B$ . We will call the point where the ramp ends and the slide starts going down as $Y$ . We can measure that the side length of the slide, or line $AY$ is equal to 15, the length of the ramp or line $BY$ is 18 and the angle between the $AY$ and $BY$ at point $Y$ is equal to $57$ degrees. If an elf skating across the rink starts at point $A$ , and their acceleration is modelled by the differential equation, $a(x)$ = $3x^2 + 6$ , where $x$ is the elf's position, and $a(x)$ is the acceleration, and we know that $v(x)$ , which is velocity, at $v(2)$ is equal to $9$ , then what is the elf's velocity when it is at point $B$ , rounded to the nearest hundredth?