Question

A Tibetan monk leaves the monastery at 7:00 am and takes his usual path to the top of the mountain, arriving at 7:00 pm. The following morning, he starts at 7:00 am at the top and takes another path back to the monastery, arriving at 7:00 pm. Show that there is some elevation that he reaches at the exact same time on both days. Hint: Let h1(t) be the monk’s elevation on the first day and h2(t) his elevation on the following day. Consider the function E(t) = h1(t) − h2(t).

Answer 1

I don't have a clue what this question wants exactly

Answer 2

okay

Answer 3

interesting okay, so no matter the weird speed he takes the point is he finished both journies in 12 hours

Answer 4

Right lol

Answer 5

we have to show there is always one point such that the elevation is the same at the same time

Answer 6

ok hang on brb

Answer 7

Yeah np

Answer 8

IVT

Answer 9

Just show that E(0) and E(12) have opposite signs and use IVT

Answer 10

Intermediate Value theorem?

Answer 11

Yup

Answer 12

How do you know you have to use that tho?

Answer 13

ok back

Answer 14

now consider 2 functions h(t)

Answer 15

its bit hard to accept that there exists such a time where the elevations will be equal tho

also was wondering what if if the monk knows teleportation..