Related Rates #5 Involving Baseball!

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Related Rates Involving Baseball!
A problem from UT Austin Calculus 1 course, HW #8.
For more free math videos, visit JustMathTutorin...

[@roseb2105]

related rates is one of those thinks watching someone else solve makes it look easy and make sense but when i have to solve myself first i go blank

[@patrickjmt]

sorry to confuse you! word problems and related rate problems can be tricky! i was going to actually make these videos private for the UT people i tutor (which is why they are a bit rushed - i have already went over the material with them) as a quick reference, but i figured i would just make them available to all.

[@Nymphaadoraa]

I like you better than KhanAcademy, you have a no-nonsense way of explaining and are very clear and straightforward whereas his videos are all +10min and a lot of useless talking. Thank you for being so smart and helpful.

[@patrickjmt]

i always try to use that procedure

[@23SuS23]

you should be a math TA here in Canada, my university pays like 50/hr for TAs!

[@minaxaArt]

Helping out even 13 years later, thank you so much.

[@chippytwang]

-20 divided by sqrt(5) can be rewritten -20 becomes -4*5 sqrt(5) in the denominator becomes 5^(-1/2) in the numerator. Then you have -4*5*5^(-1/2) Since two multiplicants share base 5, you add/subtract the powers. 1 minus 1/2 leaves 1/2 left. So it's become simplified to -4*sqrt(5)

[@vidfreakk]

U help me out before my tests allllll the time!! THankyou!!!

[@dutchiplays]

Thank you patrick you're a great help to my Quizzes and exam. I learned a lot because of you. Thumbs up!

[@toadexleen]

Thank you so much! I've been freaking out trying to solve this exact problem for homework!

[@patrickjmt]

then about 10 other people will say: you go too slow

[@normabubble]

Patrick your awesome. As long as your tutorial videos are avaible, I know i'll be okay. Thankyou so much. :)

[@splenderiffic]

thanks for helping me study for my calc test :)

[@MegaAbhishek26]

-20/sqrt5 is the same as 4sqrt5. When you conjugate -20/sqrt5 by multiplying both the num and denom by sqrt(5), you get -4sqrt5. Since the question is asking for the rate at which the distance is decreasing, the answer should be positive. That is why -4sqrt5 becomes 4sqrt5.

[@chrisrogersistheman]

@patrickJMT Yeah, I saw ACC on your website. But yeah, I hate quest. It's demoralizing when you've got four problems on it and you forget one step on just one problem and your grade plummets an entire letter. The quest problems/answers are usually greek in comparison to what we're taught and what's in the book too. You have to really understand the concepts to make some of the leaps they want you to make, I guess, but I've spent many a night watching your videos before the due date haha thanks!

[@Raffee010]

@fcmilsweeper9 (90-x) is not a constant, it's a variable because it can change.

[@patrickjmt]

@dindelicato nope, it is 100% perfect. many ways to do the problem

[@batuamparh]

thanks u sir/proff this will rly help me in the finals

[@patrickjmt]

@chrisrogersistheman i am not technically employed by UT, but it is mainly UT students that pay my bills so I do float around UT a few days each week. I feel sorry for you students taking calc at UT. It seems like a really cruddy set-up to me. Quest sucks imo.

[@viktorgoa]

nice example. thank you

[@guts6973]

When i read the problem i get lost, i can make a diagram, label everything, fivure out what the rates are, but when it comes down to using similar triangles, law of cosines, or using Pythagorean, i get messed up and overwhelmed

[@nagaprivieen2842]

thx..its a good example..

[@patrickjmt]

@23SuS23 i make more than that when i tutor ; )

[@litojonny]

related rates makes me sad

[@curioMuseum]

Ha! I thought it meant legal running distance to second base - like... actually running the bases so you don't get kicked out of the game. I guess I have to look at it like the distance from second base - how far the second baseman needs to throw the ball to hit you in the head.

[@DarkSideZombie0]

@patrickJMT how did you get from 90^2 to -1. dx/dt. i understand what you were doing but when took the derivative of 90^2 you lost me. could you help me to understand how you got -1 times dx/dt.

[@anasf911]

Thanks!! :)

[@chrisrogersistheman]

Do you teach at UT? I instantly knew that was UT homework when I saw the paper at the beginning, a suspicion then confirmed by the info bar. Here in the CNS they call it "Quest" but I don't know about the other colleges. Small world.

[@muleNHL]

When you took the derivative after you did the chain rule, why did you eliminate the constant 90^2? It seems like some of these related rate problems the constant term gets left alone and some problems it gets taken out?

[@MathMikie]

i didn't understand that at all i never know where to start with differentiation worded problems

[@patrickjmt]

@kbyrd817 hahahah. people on the internet prefer to complain though : )

[@biptrip]

can somebody please explain how to get -4sqrt of 5 pleaseeeeeeeeeeeeeeeeeeeeeeee

[@frankierivers8560]

how did you simplify that whole fraction to -4√5?

[@swatregret]

i hate related rates and you make it look so easy.. WTF! lol...

[@dia8449]

i got the same answer by keeping the smaller distance just at x , not 90- x and letting the other side as 90, only my answer was positive, is your way a more general process to use?

[@patrickjmt]

you annoy me, so i guess it all evens out.

[@TRUNKER76]

I agree. I actually skip class now and watch your videos instead! You should be paid to be the instructor!!!!

[@YEUHNBD]

whyy cant 90-x just be replaced with 45 ??

[@fcmilsweeper9]

Wait...The deriv of (90-x) is 0 if (90-x)=45...

[@Knight12ify]

How come doing x for horizontal distance (since 90-x=x) and 2x for vertical distance (since y=90=2x) gives a different answer? I get 20 square root of five by that but shouldn't it be the same?

[@rachana1212]

Patrick are you sure the answer to this problem is 4sqrt5?I got -20/sqrt5.Let me know.

[@sumalt7261]

TA's at my school get paid 12/hr

[@pstlwhppd]

@gmsherry1953 I did the same thing. I don't think you need that x there.

[@GabeSkates123]

Why is it that after you draw your triangle, you immediately know to substitute (90-x) into your pythagorian equation, rather than just writing (45)? Is it because you know that you will need to differentiate so you just use this?

[@zain4019]

and if you plug in 45 right away you get dz/dt = 0, which is obviously not right.

[@TheInvisibleRadiologist]

This is late. But that is literally the explanation. You need to relate variables to differentiate. Another option is to just say x^2 +y^2=z^2; all the sides are equal, so you can make the argument that y^2 is a constant, so it =0. So you are left with 2x(dx/dt)=2z(dz/dt), substitute x with 45, and z with z based on what you got from PTh, and you have your answer. this is one of those things in math that is more intuitive than anything. The kind of intuition you get with this kind of thing is trial and error, and not being lazy thinking. In otehr words no passive calculus.

[@5av1j]

@Jaedy16 Did you ever get a response? I don't understand the algebra part that he skipped either o_O

[@sweepmastara]

wait isnt dz/dt supposed to equal -20(sqrt 5)

[@Stuut101]

Does "DREDS" apply to all related rates problems?

[@Jukoe08]

can you also call dx/dt x'?

[@patrickjmt]

@fcmilsweeper9 nooooooooooooooooooooooooooo

[@FootDanielLight]

Rarely are people contented with everything in their lives. For example you struggle to be contented with the impatience of others. Terrible irony, eh?

[@fcmilsweeper9]

@patrickJMT Nvm figured it out : P

[@Addicti0nz1]

-1 dx/dt how did u get thatt?? i am very lost and confused..

[@miffyoreo6455]

hi sir. thanks for uploading this video. it really helps a lot. but it so hard for me to interpret other problems, it's kind of confusing... :(((((((((((((((((((((((

[@rtyrturtyrtu1702]

Woooooooooooow

[@mphomatlhabegoane9618]

I was following till you derive z^2 and still multiply it with dz/dt :/ Why?

[@jetswhiteout961]

Because he's using implicit differentiation I think

[@mphomatlhabegoane9618]

Give it a second thought

[@oblivion495]

Mpho Matlhabegoane because Z is the distance between him and the second base, we aresolving for the RATE at which Z decreases. Therefore we need to creat dz/dt becase Z is changing

[@ianmatibag4366]

Mpho Matlhabegoane review your chain rule bro.

[@hiBrianhello]

u speak faster than your other vids

[@durant3535]

good.. just slow down a little