You have inherited property in Vermont that would make an excellent ski resort. One of the slopes has a cliff on the other side of the hill, and this gives you a moneysaving idea. Instead of a chair lift or motorized tow rope, you decide to attach a pulley to the top of the cliff and then drape the tow rope over the pulley, with one end of the rope temporarily secured at the base of the ski slope and a counterweight attached to the end that hangs over the pulley at the cliff edge. The plan is to release the rope and pull two skiers (with the inertia for the pair kept between \(100 \mathrm{~kg}\) and \(200 \mathrm{~kg}\) ) up the \(400-\mathrm{m}\) slope, which has an incline angle of \(35^{\circ}\) and a coefficient of kinetic friction between skis and snow no larger than 0. 10 . You guess that customers get nervous if they move faster than \(5.0 \mathrm{~m} / \mathrm{s}\), and you wonder if a single counterweight can satisfy these constraints.