# Physics

Air resistance acting on a falling body can be taken into account by
the approximate relation for the acceleration.
a= dv/dt= g-kv, where k is a constant. A) Derive a formula for the
velocity of the body as a function of time assuming it starts from rest (v=
0 at t=0)
B) Determine an expression for the terminal velocity, which is the
maximum value the velocity reaches

Use the separation of variables integration method.
dv/(g - kv) = dt
Integrate both sides startuing from t=0, when v = 0, and you get
t = (-1/k) [log (g - kv) - log g]
-kt = log (1 - kv/g)
e^-kt = 1 - kv/g
v = (g/k) (1 - e^-kt)

When t becomes very large, v -> g/k

you suck.

1. 👍 0
2. 👎 0
3. 👁 307
1. I also didn't ask this. Again, somebody else did this.

1. 👍 0
2. 👎 0
posted by David S.

## Similar Questions

1. ### calc

Air resistance acting on a falling body can be taken into account by the approximate relation for the acceleration: a=dv/dt=g-kv where k is constnat Derive a formula for the velocity of the body as a function of time assuming it

asked by Joe on September 8, 2009
2. ### Physics

Air resistance acting on a falling body can be taken into account by the approximate relation for the acceleration: a= dv/dt = g - kv, where k is a constant. (a) Derive a formula for the velocity of the body as a function of time

asked by Rose on September 26, 2013
3. ### College Physics

A paratrooper w/ a fully loaded pack has a mass of 120kg. The force due to air resistance on him when falling w/ an unopened parachute has magnitude F(sub)d = bv^2, where b=0.14 N*s/m^2. a) if he is falling w/ an unopened

asked by Jacqueline on October 14, 2008
4. ### physics

Consider a body falling through the air. The force due to air resistance is given by, F(air)=CAv^2, where C is the coefficient of air friction, A is the area facing the direction of the motion, and V is the velocity of the object

asked by jim on April 5, 2012
5. ### Physics

A paratrooper with a fully loaded pack has a mass of 119 kg. The force due to air resistance on him when falling with an unopened parachute has magnitude FD = bv^2 where b = 0.13 (N·s^2)/m^2. The force of air resistance acting on

asked by Megan on September 23, 2009
6. ### physics

What is the net force acting on a 25-N freely falling object? What is the net force when the object encounters 15N of air resistance? When it falls fast enough to encounter 25N of air resistance?

asked by Rich on October 18, 2011
7. ### physics

If the effect of the air resistance acting on falling raindrops is ignored, then we can treat raindrops as freely falling objects. a.) Rain clouds are typically a few hundred meters above the ground. Estimate the speed with which

asked by Michel on October 27, 2016
8. ### Physics

A car drives at 15 m/s and has an air resistance force of 277 N. What is the air resistance force at 30 m/s? A truck drives at 9.7 m/s and has an air resistance force of 380 N. What is the air resistance force at 32 m/s? A 85.0 kg

asked by Becky on October 4, 2014
9. ### Physics

At about 51.2 meters/sec, a falling parachuter (before the parachute opens) no longer accelerates. Air friction opposes acceleration. Although the effect of air friction begins gradually, imagine that the parachuter is free

asked by Anonymous on February 20, 2012
10. ### Physics

a body x mass of 0.2kg moving vertically upwards has its velocity increased uniformly from 10m/s to 40m/s in just 4 sec. neglecting air resistance, calculate the upward cervical force acting on the body

asked by Dogy dogy🐕 on May 22, 2019

More Similar Questions