Three ships A, B and C are in motion. the motion of A as seen by B is with speed v towards north east.

Three ships A, B and C are in motion. the motion of A as seen by B is with speed v towards north east. the motion of B as seen by C is with a speed v towards north west. then as seen by A, C will be moving towards -
a)north
b)south
c)east
d)west
can anyone tell how to solve this ?
please. Thanks in advance

Motion of A as seen from B = vectorA - vectorB = | v | in the direction NE (45 deg to X-axis)
Motion of B as seen from C = vectorB - VectorC = | v | direction NW (135 deg to X-axis)

then, motion of C from A = vectorC - vectorA add and invert sign above eq2 , eq1

i.e., vecC - vecA = -1 x ( vecA - vecB + vecB - vecC )

= -1 x ( |v| towards NE - |v| towards NW)

= -1 x ( 2 sqrt(2) |v| towards NORTH )

= 2 sqrt(2) |v| towards SOUTH.

since multiplication with -1 inverts direction


To understand easily, plot the vector forms on a paper.

South. I found this through trial and error, but let us assume that A is moving north, B is moving West and C is moving south. In this case, an observer from B would see A to be moving North East, and from C they would see B to be moving North West. Since A and C are moving towards each other, from A, C will appear to be moving south. Hope you just needed an answer though, I can't give you a sure-fire explanation..

Edit: I guess the answer varies depending on how you place the ships. If you line them up with A on the bottom, B in the middle and C at the top you get B, but any other way and it won't work.

a) North