We will calculate the distance between the two ships as a function of time.
We can make a diagram for the situation as:
The ships are moving orthogonally, so we can calculate the distance as the hypotenuse of a right triangle.
The legs of this triangle will be the distance travelled.
As we know the speed v we can express the distance as the speed times the time: d = v*t.
We then can express the distance as:
[tex]\begin{gathered} d=\sqrt{d_1^2+d_2^2} \\ d=\sqrt{(v_1\cdot t)^2+(v_2\cdot t)^2} \\ d=\sqrt{(20.8t)^2+(25.5t)^2} \\ d=\sqrt{20.8^2+25.5^2}\cdot t \\ d=\sqrt{432.64+650.25}\cdot t \\ d=\sqrt{1082.89}\cdot t \\ d\approx32.9t \end{gathered}[/tex]Answer: the distance is approximately 32.9t (in km), given that time is expressed in hours.
