Problem

Ship

A

is located

4 \text{ km}

north and

3 \text{ km}

east of ship

B

. Ship

A

has a velocity of

20 \text{ kmh}^{-1}

towards the south and ship

B

is moving at

40 \text{ kmh}^{-1}

in a direction

37^\circ

north of east.

X

and

Y

-axes are along east and north directions, respectively a. Velocity of

A

relative to

B

(-32\hat{i} - 44\hat{j}) \text{ km/h}

b. Position of

A

relative to

B

as a function of time is given by

\mathbf{r}_{AB} = [(3 - 32t)\hat{i} + (4 - 44t)\hat{j}] \text{ km}

c. Velocity of

A

relative to

B

(32\hat{i} - 44\hat{j}) \text{ km/h}

d. Position of

A

relative to

B

as a function of time is given by

(32\hat{i} - 44\hat{j}) \text{ km}

Intuitive explanation

This is a relative velocity problem where you need to find how the ships move with respect to each other. The key insight is to work in a reference frame where one ship is stationary—subtract ship B's velocity vector from ship A's to get the velocity of A as seen from B. Then use this relative velocity and the initial separation to find when (and if) they collide or reach minimum distance.

Intuitive explanation

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