Free Fall with Air Resistance - Terminal Velocity (video 1 of 2)

Physics Ninja looks at a problem of free fall where i include air resistance effects. The resistance is taken to be linear with velocity. We solve to obtain the velocity as a function of time and verify our result with some limiting cases and find an expression for the terminal velocity.

[cassieknight]

The calculus manipulations were too complex for me, but the conclusion at the end of each calculation (initial, terminal, short term velocity situations) made sense with the calculation results. Perhaps you could create an appendix that puts in more steps so that those of us that like to play with numbers can have a chance of understanding the manipulations, even a little more. Thanks.

[justafan]

I appreciate the attempt to explain but without going step by step you just lose momentum. None of this really makes sense once you reach the integrals

[isazisempi]

As soon as I heard physics. Inja I subscribed nice job.

[dweaver]

I think you tried to simplify the calculus parts, but it made it more confusing to someone that has gone through calculus.

[diegoguevara]

Really appreciate these videos, thanks man!

[ahmethakandemir]

Hello my question is this,

Taking the air resistance into account, the acceleration of a free falling body can be described approximately by a(v)=g-av^2.
Here g is the gravity acceleration and a a constant.
Determine the velocity v(t) of the body that is released from rest.


Thank you!

[sebastiannaylor]

I didn't understand how you were supposed to integrate with an initial velocity

[Lewis-bkbr]

How would you determine a value for b? I’m doing an experiment where I have to find g from the free fall of steel balls but I also have to factor in drag and I have no idea how to determine the constant.

[samjackson]

This video was super helpful! Thanks a lot

[zamf]

Great explanation. Simple but accurate. I have one question. Suppose we don't drop the ball but propel it through the air with a certain acceleration. Can we substitute g with this new acceleration and get the same results? Also, does this mean that the terminal velocity depends on the acceleration? So, with greater acceleration we can achieve greater terminal velocity? Thanks.

[SamDOfficial]

Did you intend to write dt instead of t at 09:15? Also shouldn't it be from 0 -> t instead of from 0 -> t' ?

[delicate]

Only thing i dont understand is when you "factored" v

[kokokoko-sjex]

What if the body is a bubble under the water, 10 meters deep, for example. How will speed and acceleration be calculated, given that the size of the bubble will change and grow in each moment?

[joaohax]

How can I find out the approximated time in which Vt will be reached?

[leomadden]

Sorry but what if the body is moving down at t=0 ? Let's say at t=0, my v=8. How do I find out what is my v at t=10 ?

[Lons_Tran]

Im here to understand what d and k stand for but here i got introduce to b. I feel like i wont able to grasp it if i dont understand what each variable stand for

[ntarar]

please can u tell me how the rule becomes if the body is cube not sphere.. i really need help

[marcospimentel]

but the force is proportional to v squared not v

[omerkahyaoglu]

Can someone please explain -or tell me where to learn from- that how e^(-bt/m) became 1-(bt/m) in short time limit?

[garrettellis]

How can I find a value for b. I am dropping a basketball from different heights for my experiment and I don’t know how to find a value for b