Please help with vector (and antidifferentiation) analysis ):

[blue_snow6]

I'm really struggling. I managed to get an answer for a.i) and a.ii) but i don't know if it's right. I am completely lost from b) onwards.

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A plane carrying a skydiver travels at 200 km/h at an altitude 2000m. Find its horizontal component when:

a. dw/dt= -kw^2, where w= horizontal velocity and t = time in seconds. After 15 seconds, the horizontal velocity is 1m/s.
i. Find velocity, w, in terms of t
ii. Find the horizontal position vector, x, relative to point o.

b. let x, v and a be the position, velocity and acceleration vectors.
(the following i and j are the vector symbols)

a = (-kw^2)i + (kv^2 -g)j
v(0) = (500/9)i
x(0) = 2000j

find v and x at t time after the skydiver leaves the plane.

2.a. at the end of 15 seconds, the skydiver opens his parachute and drops vertically to the ground (no horizontal component). his final velocity is 1m/s.
Acceleration = (-p)j, where p is a constant.

find the position vector relative to the point on the ground diretly below where the parachute opens and the velocity vector, in t seconds, after the parachute opens.