Math Problem Statement
The platform for the high dive is 39 feet above the water. A diver jumps from the platform and lands in the water after 1.1 seconds. The function H(s) represents the height of the diver after s seconds. Determine the practical domain and practical range of H(s) in this situation.
Solution
The problem you uploaded involves determining the practical domain and practical range for the function , which represents the height of a diver above water after jumping from a platform 39 feet high.
Let's break this down:
- Height function, :
- The platform is 39 feet high.
- The diver lands in the water after 1.1 seconds. This means that at seconds, the height .
Practical Domain:
- The time starts from when the diver jumps, so the practical domain is from 0 to 1.1 seconds.
- seconds.
Practical Range:
- The height of the diver starts at 39 feet and ends at 0 feet when the diver lands in the water.
- feet.
Final Answer:
- Practical Domain: seconds.
- Practical Range: feet.
Would you like more details or clarification on this?
Here are 5 related questions to consider:
- How do you find the practical domain for a general height function in physics problems?
- Why is it important to focus on the practical range rather than the theoretical range?
- How would the problem change if the diver jumped from a different height?
- How can we model more precisely with a function that includes gravity's effect?
- What other real-world scenarios involve similar domain and range considerations?
Tip: When determining the practical domain, always consider real-world constraints like time or distance.
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Math Problem Analysis
Mathematical Concepts
Functions
Domain and Range
Real-world Applications
Formulas
Height function H(s)
Theorems
Domain and Range in Real-World Contexts
Suitable Grade Level
Grades 8-10