Crane and winch
The problem with a sinkhole is that the sides of the hole are unstable. You can’t just climb up the side or lower a rope down the side. This would just cause further collapse.
The answer is to get a crane. Something that sticks out over the edge of the hole, but doesn’t interact with the hole. Really, this is mostly just a nice build—but there is one physics thing to discuss.
You can’t just get a pole and stick it out from the truck and expect that pole to lift any weight of significance. It will bend or break. You need some type of structure to allow the crane to exert a torque on the end.
Here are two ways you could do that. First, you could make a type of truss. It might look something like this:
The triangle structure in the truss makes the whole thing rigid. Also, it allows multiple forces on the support end. There needs to be a force that will exert a torque to counteract the torque from the load.
The second method is to use a cable. I’m sure there is a technical term for this, but I’m just going to call it a cable. It would look like this.
I just realized that there was a mistake on the forces for the truss diagram. But you still get the idea.
Bonus, here is my initial diagram for this situation.
What about the tire and rope thing? Yes, this should work. MacGyver takes the rope and wraps it around the tire. This means that the truck’s engine can be the power to lift the humans out of the hole.
MacGyver needs to fashion a vascular clamp from some normal clamps. To do this, he builds a mini furnace. This is real. Actually, I built one of these with my daughter so that we could melt aluminum. Here is the video we started with. Note: this is awesome, but also dangerous.
This actually works. There is something amazing about melting metal with charcoal. We started off with a charcoal furnace and an old vacuum cleaner to blow in air. It works, but it goes through a bunch of charcoal really quickly. So, we switched to a propane version—this is much easier.
Bonus—here is my furnace diagram for the show.
I don’t want to write about the flash bangs—but I should say there is a legitimate basis for this. I just don’t want to tell you.