Problem $1[50$ pts$]$:

A group of hikers uses a GPS while doing a $40$ mile trek in Colorado. A curve fit to the data shows that their altitude can be approximated by the function, $y(t)=0\mathrm{.}12t^5-6\mathrm{.}75t^{4}135r^3-1120r^{2}3200r9070$ where $y$ and $t$ are expressed in feet and hours, respectively. During the $18$ hour hike, determine $($a$)$ the maximum altitude that the hikers reach, $($b$)$ the total feet they ascend, $($c$)$ the total feet they descend. Hint: You will need to use a calculator or computer to solve for the roots of a fourth onder polynomial.

Problem $2[50$ pts$]$:

The motion of a particle is defined by the relation $x=t^3-6t^{2}9t5,$ where $x$ is expressed in feet and $t$ in seconds. Determine $($a$)$ when the velocity is zero, $($b$)$ the position, acceleration, and total distance traveled when $t=5s.$