Lec-3: Related rates examples| Ladder and Shadow problems
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#Nommathex # related rates #calculus #shadow examples # Differentiation
“Welcome back to our channel! In this video, we’ll be solving two classic related rates problems: the ladder problem and the shadow problem. These problems are excellent examples of how we can use derivatives to analyze real-world situations where different quantities are changing over time.
We’ll break down each problem step by step, walking through the process of setting up equations, differentiating, and solving for the unknown rates. By the end, you'll have a clear understanding of how to approach and solve these types of related rates questions.
If you're looking to master these tricky problems for your exams or just want to sharpen your calculus skills, this video is perfect for you!
Course: Calculus
Topic: related rates ladder and shadow problem
Text: Calculus & Analytic geometry by Tomas, chapter: 3
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1. A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving at the rate of 5 ft sec.
a). How fast is the top of the ladder sliding down the wall then?
b). At what rate is the angle between the ladder and the ground changing then?
2. A 1.8-meter-tall man walks away from a 6.0-meter lamp pole at the rate of 1.5 m/s. The light at the top of the pole casts a shadow in front of the man. At what rate is the tip of the shadow moving (a) away from the person (b) away from the pole?
3. A spot light is on the ground 20 ft away from a wall and a 6 ft tall person is walking towards the wall at a rate of 2.5 ft/sec. How fast is the height of the shadow changing when the person is 8 feet from the wall? Is the shadow increasing or decreasing in height at this time?