Flaming Torch

Congratulations, your boulder hit the three poachers perfectly and knocked them down the hill! They are lying unconscious on a ledge about 300 feet down. You have at least a half hour to explore the cave before they wake up.

You will need some light inside the cave so you decide to make a flaming torch using rope and melted bees wax. To get enough brightness, you should have at least 200 cm² of rope on the outer layer. To have your torch last for 30 minutes, you should have at least 40 mL of bees wax soaked into the rope. The rope can hold 10% of its volume in bees wax. Your stick is 3 cm in diameter and your rope is 1 cm in diameter. How many rows of rope up and down (R) and how many layers (L) should your torch have?

Pendulum Trap

Congratulations, you took the path to the left and arrived at the dwarf island bear cave 18 minutes before the poachers! You found bear tracks outside the cave, but no bears in the entrance. You need time to explore the cave

Fortunately, there is a large, sturdy tree directly above the cave and a large boulder off to the side up on the hill.  You tie a rope to the boulder and the tree and wait for the poachers. When they approach the cave, you will release the boulder and protect the bears, but the timing must be perfect. How many seconds before they reach the cave entrance should you release the boulder?

Hint: The time for a complete swing of a pendulum is given by T below.  L is the length of the pendulum and g is the gravitational acceleration, which for earth is 9.8 m/s².