You and your friends pull your car off a mountain road onto an overlook to take pictures of the frozen lake below. You lose your footing on the packed snow, fall over the cliff , and land in a soft snow bank on a ledge, 10 feet below the edge. The cliff ’s wall is too smooth to climb upwards and too steep and dangerous to climb the remaining 300 feet to the bottom. While trying to think your way out of your predicament, you realize one reason you had slipped was that you had misjudged how the cliff sloped towards the edge (a decline of about 5–10 degrees). There is nothing near the edge to which your friends can tie a rope, and they fear the footing is too slippery for them to pull you to the top. However, they can get the car close enough to the edge to tie the rope to the bumper and hang it over the edge. You are worried, however, that the car might slip over the edge as well. On your phone (which has survived the fall) you look up the coefficient of static friction of snow tires on packed snow and find that it ranges from 0.22 to 0.26, and that the model of your friends’ car weighs 3856 lb. Your own weight fluctuates between 120–130 lb.

(a) What is the worst-case scenario in terms of the parameters given?

(b) Assuming the worst-case scenario, should your friends bring the car close to the edge?

(c) Next, should you risk tying the rope to the trailer hitch and trying to climb out? You assume the hitch is low enough to the ground so that the tension force is parallel to the slope near the edge of the cliff and that you climb up the rope at a constant velocity.