A $2$ lb rocket is launched from the ground, with its launch rail elevated at an angle of $70$

from ground, with zero initial speed. The rail length is set at $3$ ft$.$ Assuming its motor provide

a thrust force T $=25$ lb for the period of $0$ t $0\mathrm{.}1$s and T $=0$ for t $^30\mathrm{.}1$ s$,$ no air resistance,

constant gravitational acceleration g $=32\mathrm{.}2$ ft$/$s $2,$ a kinetic friction coefficient k $=0\mathrm{.}2$

between the rocket and launch rail and a particle model for the rocket, find t$3=$ time when it

lands on a flat ground. Also, find its range i$.$e$.$ x$($t$3).$ Use its position at t $=0$ as the origin $($x$=$

$0$ and y $=0)$