It is clear from the diagram that the shortest distance between the ship \\\\(A\\\\) and \\\\(B\\\\) is \\\\(PQ\\\\).Here, \\\\(Sin\\,45^0=\\dfrac{PQ}{OQ}\\\\)\\\\(\\implies PQ=100\ imes \\dfrac{1}{\\sqrt 2}=50\\sqrt 2\\,m\\\\)Also,\\\\(V_{AB}=\\sqrt{V_A^2+V_B^2}=\\sqrt{10^2+10^2}=10\\sqrt 2\\,km/h\\\\)So, the time taken to reach shortest path is\\\\(t=\\dfrac{PQ}{V_{AB}}=\\dfrac{50\\sqrt2}{10\\sqrt 2}=5\\,h\\\\)