Question

a square swimming pool ABCD, a man is going to get to C from A, if he is going to walk,the velocity of walking is W,if he is going to swim,the velocity is M，so what he should do to get C with the shortest time?

Answer 1

oh i forgot something ( 1.W/M>\[\sqrt{2}\] 2.W/M<\[\sqrt{2}\]

Answer 2

i need a graph to show how he should do

Answer 3

\[\min\{\frac{2s}W,\frac{s\sqrt{2}}{M}\}\]

Answer 4

#1 would make it more effective to walk, while #2 would instead make swimming faster.

Answer 5

@bahrom7893

Answer 6

let W/M = k or W= k M
when is it faster to swim than walk, as a function of k?
compare the time to swim to time to walk (replace walking speed with k*M):
\[ \frac{s\sqrt{2}}{M} < \frac{2s}{kM} \]
solving for k, we find
\[ k <\sqrt{2} \]
so it is faster to swim when W/M < sqrt(2)
otherwise, it is faster to walk