Question

A ball of mass 5 slugs is dropped from a height of 1000ft. Find the limiting velocity of the ball if it encounters a force due to air resistance equal to (-1/2)v.

Answer 1

whats limiting velocity? do they just want the velocity function in terms of t

Answer 2

Force of gravity is mass* acceleration
ma = 5*(-32) = -160
Force of air resistance is -(1/2)v
Net force:
-160-(-1/2v) = (1/2)v -160
Net acceleration, divide by the mass:
a = (1/10)v - 32
Net velocity: **initial velocity is zero**
v = (1/10)v*t -32t
solve for v:
v -(1/10)vt = -32t
v(1-(1/10)t) = -32t
v = -32t/(1-(1/10)t)

Answer 3

If you then take the limit as t goes to infinity.
multiply top and bottom by 1/t
lim = -32/(1/t -1/10) -> lim 1/t = 0
lim = -32/-1/10 = 32*10 = 320

Then limiting velocity would be 320 ft/sec
*If thats what they mean*

Answer 4

you may want another opinion, im not as confident in my physics i hope i did this right

Answer 5

This is correct, I just checked :)

Answer 6

ok good to hear :)