💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Oh no! Our educators are currently working hard solving this question.

In the meantime, our AI Tutor recommends this similar expert step-by-step video covering the same topics.

Like

Report

Numerade Educator

Like

Report

Problem 49 Easy Difficulty

When a raindrop falls, it increase in size and so its mass at time $ t $ is a function of $ t, $ namely, $ m(t). $ The rate of growth of the mass is $ km(t) $ for some positive constant $ k. $ When we apply Newton's Law of Motion to the raindrop, we get $ (mv)' = gm, $ where $ v $ is the velocity of the raindrop (directed downward) and $ g $ is the acceleration due to gravity. The terminal velocity of the raindrop is lim $ _{t \to \infty} v(t). $ Find an expression for the terminal velocity in terms of $ g $ and $ k. $

Answer

$$\lim _{t \rightarrow \infty} v(t)=g / k$$

Discussion

You must be signed in to discuss.

Video Transcript

we have radar. Yeah. Okay. Well, K's no, they were really Will do. Yeah. Uh, we any with d n r for that we have is equals to And the your dd v m. Now I m ready that we Yeah, you are me love. Okay, you were G. It is our second you hear me? Let the Jonah last seen. And this now infinities. Then the minute you telling me do you want me and you deaf in pretty do your duty last week is equal to a man. You're being really easy now. As you know, this is zero laugh. Kids remain destiny. Really? TV is the, uh, the solution as living to 10 million Bernie, be well do you want? So it is that some of the last is even as do your which is the answer into the