v(t)m/s be the velocity of the body at time t in seconds. Assume that v is positive in the downward direction – that is, when the object is falling. We assume that the forces acting on the body are the force of gravity and a retarding force of air resistance with direction opposite to the direction of motion and with magnitude proportional to the square of the velocity. Let c be the constant of proportionality.
Question
Supposed a body of mass 22 kg is falling in
the atmosphere near sea level.
Let v(t)m/s
v(t)m/s be the velocity of the body at time t in seconds. Assume that v is positive in the downward direction – that is, when the object is falling. We assume that the forces acting on the body are the force of gravity and a retarding force of air resistance with direction opposite to the direction of motion and with magnitude proportional to the square of the velocity. Let c be the constant of proportionality.
The gravitational constant is g=9.8m/s
a) Find a differential equation for the velocity v
v:
dv
dt
=
(b) Determine the limiting velocity after a long time. Your answer should be an expression in c
c.
limiting velocity
m/s
(c) Find the drag coefficient,c
, so that the limiting velocity is 41m/s
c =
kg/m
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