$(7)$ Chapter $8$ Problem $15.$ An automatic dryer spins wet clothes at an angular speed of $4\mathrm{.}8ra\frac{d}{s}.$ Starting from rest, the dryer reaches its operating speed with an average angular acceleration of $3\mathrm{.}6ra\frac{d}{s^2}.$ How long does it take the dryer to come up to speed?

$(7)$ Chapter $8$ Problem $19.$ A gymnast is performing a floor routine. In a tumbling run she spins through the air, increasing her angular velocity from $3\mathrm{.}00$ to $5\mathrm{.}00re\frac{v}{s}$ while rotating through one$-$half of a revolution. How much time does this maneuver take?