relative velocity and vectors? (question in comments)

Question

anonymous · Answer

In this question, i is a unit vector due east and j is a unit vector due north.
At 0900 hours a ship sails from the point P with position vector (2i + 3j) km relative to an origin O.
The ship sails north-east with a speed of 15 2 km h–1.
(i) Find, in terms of i and j, the velocity of the ship. [2]
(ii) Show that the ship will be at the point with position vector (24.5i + 25.5j) km at 1030 hours. [1]
(iii) Find, in terms of i, j and t, the position of the ship t hours after leaving P. [2]
At the same time as the ship leaves P, a submarine leaves the point Q with position vector
(47i – 27j) km. The submarine proceeds with a speed of 25 km h–1 due north to meet the ship.
(iv) Find, in terms of i and j, the velocity of the ship relative to the submarine. [2]
(v) Find the position vector of the point where the submarine meets the ship. [2]

anonymous · Answer

If the ship is travelling NE, the direction will be i+j.  The magnitude of this vector is 15.2.  The 15.2km/hr magnitude is shared equally between the East and North directions.  We have:
x^2+y^2=(15.2)^2
2x^2=(15.2)^2
x=y=$$\frac{15.2\sqrt{2}}{2}$$So we can describe the velocity vector as:$$\vec v=\frac{15.2\sqrt{2}}{2}(i+j)$$

anonymous · Answer

I dont' get the position vector (24.5i+25.5j) after 1.5 hours of travel.  Are your values correct?

anonymous · Answer

The speed is 15.2km/hr, correct?

anonymous · Answer

the values are correct i got them from a question paper

anonymous · Answer

Is my value for velocity vector correct?

anonymous · Answer

sorry i don't remember i posted this question a long time ago :P