Two ships, a and b, leave port at the same time. ship a travels northwest at 24 knots, and ship b travels at 28 knots in a direction 40 degrees west of south. (1 knot-1 nautical mile per hour) what are the
(a) magnitude and
(b) direction of the velocity of ship a relative to b?
(c) after what time will the ships be 160 nautical miles apart?
(d) what will be the bearing of b (the direction of b's position) relative to a at that time?

a) V=38.51knots

b) 88.5 degrees north of east

or 1.5 degrees east of north.

c) 4.15 hours

d) 88.5 degrees South of west

or 1.5 degrees West of South.

Explanation:

Fisrt of all, we need to find the X and Y components of the velocity of each ship.

for ship A:

Now for B:

the relative velocity is given by:

For the X axis:

For the Y axis:

And the magnitud is given by:

We can calulate the angle using :

that is 88.5 degrees north of east

or 1.5 degrees east of north.

In order to know the time the ships will be 160 nautical miles apart is given by:

Because the velocity of A relative to B will be the opposite, so will be its direction.

So the angle will be:

88.5 degrees South of west

1.5 degrees West of South.

see earlier answer

the answer to this is proletariats.

hope this : )