Hydrodynamic drag force density velocity

[cheff3r]

Homework Statement

A steel sphere in a tank of oil is given an initial velocity v = 2i (m/s) at the origin of the coordinate system shown (if you don't trust the attached image it is essenital). The radius of the sphere is 15 mm. The density of the steel is 8000 kg/m3 and the density of the oil is 980 kg/m3. If is the sphere’s volume, the (upward) buoyancy force on the sphere is equal to the weight of a volume of oil. The magnitude of the hydrodynamic drag force D on the sphere as it falls is |D| = 1.6|v| N, where |v| is the magnitude of the sphere’s velocity in m/s.

a) What are the x and y components of the sphere’s velocity at t = 0.1 s?
What are the x and y coordinates of the sphere at t = 0.1 s?

Homework Equations

Mass=Volume * Density
Volume of shere=4/3*Pi*r^3
F=ma
plus any others that i haven't used

First Quesetion it say velocity=2i (m/s) what's with the i is it the ijk vectorso in the x direction?

The Attempt at a Solution

a) Volume of shere=4/3*Pi*0.015^3=4.5Pi*10^-6
Mass=V*D=4.5Pi*10^-6*8000=0.036Pi
F=ma=0.036Pi*Second problem here gravity isant going to be 9.81 because its in oil
i was next going to use K.E.=1/2*mv^2


secound way i condsiered was finding mass as above but v=u+at
but yet again i don't know its accelereation

i'm considering the idea that my teacher has expected more assumed knowledge from the students because i don't know what use the hydrodynamic drag force would be used for,
is it the same as normal drag force? if that the case is the question something to do with drag force being proportional to velocity (this is a logical guess is it proportional?)

if you can help me with part a first, i will have another attempt at b

 

[cheff3r]

okay my teacher has still left this question as a challenge question(which were allowed to get help on), but he has given us a couple hints;

for part a you need to create an euation which will be of type seperable first order linear (which is easy enough for me to understand but my problem is still at the first part how do i create the first question?)

and also he gave us a little diagram which is pretty straight foward to explain, it was of the drag force and initial velocity and weight all separated into its vectors (no numbers given)