Answer:
[tex]v = 12.44 Knots[/tex]
Explanation:
First ship starts at Noon with speed 20 Knots towards West
now we know that 2nd ship starts at 6 PM with speed 15 Knots towards North West
so after time "t" of 2nd ship motion the two ships positions are given as
[tex]r_1 = 20(t + 6)\hat i[/tex]
[tex]r_2 = 15(t)(cos45\hat i + sin45\hat j)[/tex]
now we can find the distance between two ships as
[tex]x = \sqrt{(20(t + 6) - 10.6 t)^2 + (10.6t)^2}[/tex]
now we have
[tex]x^2 = (120 + 9.4 t)^2 + (10.6 t)^2[/tex]
[tex]x^2 = 200.72 t^2 + 14400 + 2256 t[/tex]
now we will differentiate it with respect to time
[tex]2x\frac{dx}{dt} = 401.44 t + 2256[/tex]
here we know that
[tex]t = \frac{90}{15} = 6 hours[/tex]
so we have
[tex]x = 187.5[/tex]
now we have
[tex]2(187.5) v = 401.44(6) + 2256[/tex]
[tex]v = 12.44 Knots[/tex]
