Answer
33 hp engine is required.
Work Step by Step
The forces opposing the motion of the skier are the component of weight directed down the slope and the force of friction. We can find the force $F$ exerted by the rope as follows:
$F = mg~sin(\theta) + mg~cos(\theta)\cdot \mu_k$
$F = (65~kg)(9.80~m/s^2)~sin(23^{\circ}) + (65~kg)(9.80~m/s^2)~cos(23^{\circ})(0.10)$
$F = 307.5~N$
We can use this force to find the power provided by the engine. Since there are 30 skiers, we need to multiply by 30 to find the total power $P$:
$P = 30\times \frac{F\cdot d}{t} = 30\times \frac{(307.5~N)(320~m)}{120~s} = 24,600~W$
We can convert this power to units of hp:
$P = (24,600~W)(\frac{1~hp}{746~W}) = 33~hp$
Therefore, a 33 hp engine is required.
