The problem is:
A snowball is dropped from the top of a building, evaporation causes the mass m of the snowball to decrease at a rate proportional to the snowball's speed as the snowball falls, so that
M' = k * abs(y')where y denotes the vertical distance from the ground and k is a negative constant.
Derive the differential equation governing y(t), neglecting all physical phenomena except the pull of Earth's gravity on the snowball and the variation in the snowball's mass
This is what I have been able to work out:Position = 0i + y(t)j
v = d/dt(position) = y'(t)
Using newtons Second law
Net force = (d/dt)[(mass)(velocity)]
-m(t)g = (d/dt)(m(t)y'(t))
-m(t)g = m'(t)y'(t)+m(t)y''(t)
And I'm not able to simplify this expression so I must be missing something in the setup...Any help would be great.