At noon, ship a is 30 nautical miles due west of ship
b. ship a is sailing west at 22 knots and ship b is sailing north at 23 knots. how fast (in knots) is the distance between the ships changing at 5 pm? (note: 1 knot is a speed of 1 nautical mile per hour.)
We need to find relative speed between two ships. We look at relative speed along the north direction and west direction. [tex]N: v_b_n-v_a_n=v_b_n\\ W:v_a_w-v_b_w=v_a_w\\[/tex] This is because boats are travaling at directions that are perpedincular to each other. Total relative speed is: [tex]v_r=\sqrt{v_a_w^2+v_b_n^2}=\sqrt{22^2+23^2}=31.83[/tex] And that is how fast they are moving away from eachother. Please note that these boats are not accelerating, therefore the distance between them is increasing at the constant rate.
