The Animorphs are planning a trip to the Yeerk pool! In Animorphs # 17, The Underground, they must dig a long tunnel in mole morph. Let's help them plan out their trip with math! Their tunnel is dug in shifts and at a downward angle. On their return trip, they must dig out a turn around point and then ascend to the surface. I will share my solutions in a week or so if anyone is interested on trying out a solution of their own.
Note: On pages 94 & 95, it turns out the Animorphs frequently encounter rocks they must go around and at about 25ft deep they luckily find a cave and can stop digging. For simplicity we will pretend they can just dig in a straight line to their destination.
a) Given their 2 hour time limit in mole morph, and assuming an average walk speed, w, what is the maximum length tunnel they can dig while being able to safely return to surface?
b) On page 93, Ax, Tobias, and Marco discuss how long it will take them to complete the tunnel. They estimate that the Yerk pool is 50 feet below ground and that for every 6 feet of tunnel, they dig 1 foot down. Assuming they can maintain this ratio, how much tunnel will they need? Hint: Sin(θ) = 1/6
c) Given the length of tunnel required to reach the Yerk pool, what is the minimum walk speed required for the Animorphs to be able to safely walk down the tunnel and come back in time to demorph?
d) Rachel is the first person to start digging. She gets off to a rocky start but for simplicity, let's assume she begins to dig the tunnel immediately and continues until it’s time to return to the surface. They decide to take one hour shifts (page 91). If Rachel digs at a rate of r feet per second and must walk back up the length of the tunnel in 1 hour, how much tunnel length can she create? Solve symbolically (don't put in numbers just yet).
e) According to various pest control companies online, moles can dig at a maximum rate of about 15 inches per hour. Using this rate, and the walk speed estimated in a), how long is the tunnel from d)? (Plug in numbers now :) )
f) Hardest (but most fun???) The Animorphs take shifts digging. They must descend to the bottom of the tunnel, dig for some time, dig a turn around point, and finally ascend back to the surface. If they must return to the surface in 1 hour, what is the length shift N can dig? Note that each shift spends less time digging due to the extra tunnel length they must traverse.
e) If nothing had gone wrong >_> and the Animorphs were able to dig in a straight line, how many dig shifts would it have taken for them to dig 50 ft deep?
I don’t expect anyone to attempt a solution but I’ve been thinking about this all week. This is the only way I can put my mind at ease.














