# Position Vectors: Boat A&B Initial Pos, Velo Vector & Angle

• SSUP21
In summary, Boat A's initial position is (3,-4) km and Boat B's initial position is (4,3) km. The velocity vectors for both boats are given by vA = (-1,2) km/h and vB = (-3,-2) km/h. The angle between their paths can be calculated using the formula for the angle between two vectors. The boats are closest to each other when t = 1 hour.

#### SSUP21

Boat A's position is given by the parametric equation x=3-t, y= 2t -4 where position is km and time is hours. Boat B's poisiton is given by x=4-3t, y= 3-2t

a) find the initail position of each boat
b) find the velocity vector of each both
c) what is the angle between the paths of the boat
d) at what time are the boats closest to each other

I have NO CLUE on how to start the question

SSUP21 said:
Boat A's position is given by the parametric equation x=3-t, y= 2t -4 where position is km and time is hours. Boat B's poisiton is given by x=4-3t, y= 3-2t

a) find the initail position of each boat
b) find the velocity vector of each both
c) what is the angle between the paths of the boat
d) at what time are the boats closest to each other

I have NO CLUE on how to start the question

1) t is a variable representing time in hours and (x,y) is the boat's position in km relative to some arbitrary coordinate system. Initial time is usually assumed to be when t = 0...so find x and y when t=0 to answer the first question.
2) Velocity is a vector telling you what direction it's moving in, so it is equivalent to the gradient of position. In other words, v = ( dx/dt, dy/dt ).
3) Google "angle between two vectors"
4) The boats are closest together when the squared distance between them is smallest (squared distance is easier to calculate than Euclidean distance). Try writing a new parametric equation of distance