Problem
Set 3: Problem 3.
Problem:
A test projectile is fired horizontally into a viscous liquid with initial velocity
v
o
. The drag
force,
D
, on the projectile is
D
=
−
mkv
2
, where
m
is the projectile’s mass,
v
is instantaneous velocity
and
k
is a constant of dimensions length
−
1
. Assume the motion is so rapid that any vertical deflection
due to gravity is negligible.
(a) Determine the velocity of the projectile in terms of
v
o
,
k
and
t
and compute the time at which
the projectile’s speed is
1
2
v
o
.
(b) Determine the projectile’s instantaneous position,
x
, as a function of
v
,
v
o
and
k
.
Solution:
Newton’s Second Law tells us that
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 Spring '06
 Shiflett
 Force, Velocity, vo Vo, vo kt vo

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