HW$03\mathrm{.}1-$ For the first $20$ seconds, the wheel rotates with an angular velocity of $(t)=\sqrt[\phantom{2}]{0\mathrm{.}8t}ra\frac{d}{s},$ where $t$ is in seconds. After $t=20s,$ the angular velocity of the wheel is constant at $4ra\frac{d}{s}.$ Determine the time at which the bucket will be hoisted $s=70ft$ if $s=0$ at $t=0.$