Vectors question?

Question

A boat starts from the position (600, - 300) [in part a, the boat's position at time t was (-t + 600, 2t - 300)] and is pointed in the direction N 4Odeg W. Its speed in still water is 2ms^-1, but it
sails in a current of speed 0.5 ms^-1 flowing towards the direction
S 20deg W. Take i to be 1ms^-1 due east and j to be 1ms^_1 due north

ok for the resultant velocity I got v = -1.4566i + 1.062j

i'm stuck on these two questions:

Use the resultant velocity to write down expressions in terms of t
for the x and y coordinates of the boat at time t

Find the distance between the boat an the island position (200, 100)
at the moment when the boat is due south of this position.

the position, i got when the boat is south of the island is (200, -8.362).

Answer 1

let Vb be velocity of boat
Vb = (-2)[.cos50°.i + sin50°.j.]
Vb = - 1.29.i + 1.532.j
Let Vs be velocity of stream
Vs = - 0.5cos70°.i - 0.5.sin 70°.j
Vs = - 0.17.i - 0.47.j
Let resultant velocity = Vr (vector)
Vr = Vb + Vs
Vr = - 1.46.i + 1.06.j (as per your solution)

Distance = velocity x time
Let time = t sec
Distance west from start position = 1.46.t
Distance north from start position = 1.06.t
Co ordinates are (600 - 1.46t),(-300 + 1.06t)
Boat starts at S(600,- 300) and when it is due south of island(200,100) it will have travelled 400 m west
Let time = t seconds
Horizontal component of velocity is 1.46
X = Horizontal distance (from S) = 1.46.t
Vertical component of velocity is 1.06
Y = Vertical distance (from S)= 1.06.t
Let Ø = angle boat path makes with horizontal
1.46.t = 400
t = 274 sec
Horizontal distance = 400 m
Vertical distance = 1.06 x 274 = 290 m
Distance (D) between island and boat = 100 + (300 - 290)m
D = 110 m

Answer 2

If I believe your velocity.

Position = position initial + velocity times time (constant v)

(x,y) = (600,-300) + (-1.4566,1.062) times time

So when the boat is due south of (200,100), y = 100

Plug that into your equation for y to solve for time.

Then plug in that time to find x.

Then subtract that x from 200 to get your answer.

Make sense?

Answer 3

hard question, easy if i will understand it. You will have to find everything by projecting. Do not expect nice answers because there will be some cos(40)involved