Problem $14\mathrm{.}9$ The $170-lb$ skier is schussing on a $25$

slope. At the instant shown, he is moving at $40f\frac{t}{s}.$ The

kinetic coefficient of friction between his skis and the

snow is ${}_k=0\mathrm{.}08.$ Aerodynamic drag exerts a resisting

force on him of magnitude $0\mathrm{.}015v^2,$ where $v$ is the mag$-$

nitude of his velocity. If he makes no attempt to check

his speed, how long does it take for it to increase to

$60f\frac{t}{s}?$