Problem $3$: $(10$ points$)$

The kicker for the Chico State football team kicks a football $($from the ground$)$ with an initial speed of $20\mathrm{.}6\frac{m}{s}$ at an angle of $\frac{5}{16}$ above the horizontal. Use $g=-9\mathrm{.}81\frac{m}{s^2}$ for the acceleration due to gravity.

a$)[6$pts$]$ Build parametric equations for the path of the football. Be sure to include the domain of $t$ values that makes sense for your equations.

b$)[4$pts$]$ Find both the horizontal and vertical velocities of the football $3$ seconds after it is kicked. Be sure to include units.