- #1
AaronKnight
- 10
- 0
Homework Statement
A raindrop is falling through a cloud, collecting water as it falls. If the raindrop has mass
m and velocity v, show that
mg = vdm/dt +mdv/dt.
Assume that the drop remains spherical and that the rate of accretion is proportional to the
cross-sectional area of the drop multiplied by the speed of fall. Show that this implies that
dm/dt = kvm2/3,
for some constant k. Using this equation and the assumption that the drop starts from rest
when it is infinitesimally small, find m as a function of x. Hence show that the acceleration
of the raindrop is constant and equal to g/7.
I have managed to show that mg = vdm/dt +mdv/dt easily, but I am at a lose for the second part where the question asks "Show that this implies that dm/dt = kvm2/3".
I am unsure where to begin, any help in pointing me in the right direction would be greatly appreciated.
Thank you.