Q$3)(20$ pts$)$ A test platform to study potential$-$kinetic energy transformation is being constructed. Platform consists of $2$ Bezier Surfaces shaped by $C_1(t)$ and $C_2(t)$ Bezier Curves. $C_1(t)$ is a $5^{th}$ degree Bezier Curve and shown in the figure. A Cubic Bezier Curve $C_2(t),$ that follows $C_1(t)$ is designed to be the second curve. The surface is designed such that $C_1(t)$ and $C_2(t)$ have tangencial $(G_1)$ continuity between them, the second line of $C_2(t)\text{'}$s control polygon is on $x+3=2Y$ line, Last line of $C_2(t)$ Bezier Polygon is parallel to $x=-Y$ line. The last control point of $C_2(t)$ is $P_3=(6,0,0).$

Answer the questions below with respect to this explanation.

a$)(2pts)$ Identify the control points of the curve, $C_2(t)$

$C_2(t)$:$P_0$:

$P_1$ :

$P_2$ :

$P_3$ :

Units are in meters.

Only $C_2(t)$ must be drawn in a grid paper with $1$:$100$ scale.

Each square in grid is $5mm5mm$

b$)(6$ pts$)$ Write the polynomial form of the curve, $C_2(t)$