Question

Capt. Hooke is on a treasure hunt. His GPS shows him that he is 25 m away from what he is looking for. He walks 25 m towards west. The GPS compass now tells him that the treasure is due south from where he is standing. How far south does he need to go to discover it?

Answer 1

Capt. Hooke goes 25m south

let's say he needed to go x m south

Hence total distance from start

$=\sqrt{25^2+X^2}$

25m away it was from starting hence

$\sqrt{25^2+X^2}=25\\\implies X=0$

Therefore, Capt. Hooke does not need to walk any more distance. He just needs to rotate 90 degrees on the left.