At 3 pm ship A is 20 nautical miles south west of ship B. Assuming that the y- direction is north and the x-direction is east, the velocities of ships A and B can be expressed in knots in vector form as
Va=(12,+5) Vb=(-8,-9)
(i) Find the velocity of ship B relative to ship A
To find the velocity of ship B relative to ship A, you need to subtract the velocity of ship A from the velocity of ship B.
Given that the velocity of ship A is Va=(12,+5) and the velocity of ship B is Vb=(-8,-9), the velocity of ship B relative to ship A (Vba) is calculated as:
Vba = Vb - Va
Substituting the values:
Vba = (-8,-9) - (12,+5)
To subtract two vectors, you need to subtract their corresponding components:
Vba = (-8-12, -9+5)
Simplifying:
Vba = (-20, -4)
Therefore, the velocity of ship B relative to ship A is Vba = (-20, -4) knots.