OpenTube

Related Rates - The Shadow Problem

The Organic Chemistry Tutor

721,227 views

This calculus video tutorial explains how to solve the shadow problem in related rates. A 6ft man walks away from a streetlight that is 21 feet above the ground at a rate of 3ft/s. At what rate is the length of the shadow changing?

Related Rates - Free Formula Sheet:
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Calculus 1 Final Exam Review

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Introduction to Limits:
Calculus 1 - Introduction to Limits

Derivatives - Fast Review:
Calculus 1 - Derivatives

Introduction to Related Rates:
Introduction to Related Rates

Derivative Notations:
dy/dx, d/dx, and dy/dt - Derivative Notati...

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Related Rate Problems - The Cube - Volume,...

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Inflated Balloon & Melting Snowball:
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Gravel Dumped into Conical Tank:
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Related Rates - Area of a Triangle:
Related Rates - Area of a Triangle

Related Rates - The Ladder Problem:
Related Rates - The Ladder Problem

Related Rates - The Distance Problem:
Related Rates - Distance Problems - Applic...

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Related Rates - Airplane Problems:
Related Rates - Airplane Problems

Related Rates - The Shadow Problem:
Related Rates - The Shadow Problem

Related Rates - The Baseball Diamond Problem:
Related Rates - The Baseball Diamond Problem

Related Rates - The Angle of Elevation Problem:
Related Rates - Angle of Elevation Problem

Related Rates - More Practice Problems:
Related Rates - Conical Tank, Ladder Angle...

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20 Comments

@TheOrganicChemistryTutor Creator 3 years ago (edited) Pinned

Related Rates - Free Formula Sheet: https://www.video-tutor.net/calculus-formula-sheets.html
Final Exams and Video Playlists: https://www.video-tutor.net/
Final Exam and Test Prep Videos: https://bit.ly/41WNmI9
Calculus 1 Final Exam Review: https://www.youtube.com/watch?v=WmBzmHru78w
Next Video: https://www.youtube.com/watch?v=zytwFSyH0_0&list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv&index=105

@shr1mpy194 5 years ago

Bruh I learn more from u in 10 minutes than I do from my teacher in 10 classes. TYSM

@liezyldavila306 6 years ago

for those who are asking why 8ft from the street light is not included in part a. it turns out that as long as the man is moving at a constant rate, the rate of his shadow will also remain constant at 6/5 ft/sec. regardless of how
far away he is from the street light.

@sabrinabong9320 2 years ago

saved me. i owe you my firstborn child.

@merkov8715 3 years ago

I can't even believe I am now capable of solving these type of problems on my own. Thanks a lot man.

@brettmartin536 7 years ago

you r actually so good at explaining

@hansonji9578 6 years ago

everytime I face a difficult problem in calculus, your always here for me. Your the real MVP

@ptyptypty3 4 years ago

for what it's worth.. the the rate at which the tip of the shadow is moving is equal to the Given velocity of the man walking PLUS the rate at which the shadow is moving. So, dx/dt + ds/dt is all you need. NO need to calculate using dL/dt. This was an extra step that was worthwhile to see. It's always good to see extra steps to learn as much about how a problem can be solved. GREAT VIDEO as USUAL.. You're the best!!! thanks for all the effort you've invested in all your videos...

@mastershrew82 5 years ago

I love how he just ends with, "Yeah these other values are irrelevant". Thank you god for sending this angel to explain work made by assholes

@gabriel9668 6 years ago

How do you know math so well? And how are you able to teach is so well? I've watched several of your videos and found each one very helpful. Thank you! I also comment and like every video of yours I watched, you know, for the youtube algorithm, but your videos are always the first to pop up, so I guess I am doing it because I really appreciate what you do.

@samriddhamalla6046 7 years ago

i have a feeling i will be getting this problem in the final

@Pushed2InsanityYT 6 years ago

Thanks a lot....i wasn't able to solve the first part by myself, but after understanding it, i was able to solve the second part by myself :) Whenever you guys solve these related rates problems, your first step should be to make a diagram and find an equation which relates both the variables which are changing w.r.t time! Good Luck :)

@Nathanator 2 years ago

Got an exam in 15 minutes, this video was more helpful than my teacher’s lessons, thank you

@TOPCricket-ku8sc 11 months ago

wow you really saved me 1 hour and 30 before my test

@JonathanBrown-emboldened 3 years ago

5 years later and you are still saving lives!

@Say_Tin 2 years ago

This is more helpful than my calculus course right now lmao

@georgesadler7830 3 years ago (edited)

MR. Organic Chemistry Tutor, this is another solid explanation of Shadow Problems in the Related Rates section of Calculus One. Calculus has some great Related Rates problem in its library. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.