Please solve 1 and 3 ### Educational Website Transcription#### Problems Set1. **Land Excavation Calculation** - One hectare, a unit of measure often used in measuring land areas, is defined to be \(10^4 \, \text{m}^2\). A student in China excavates a pit 15 m deep over an area of 3 hectares. How much earth does he manage to exhume? Express your answer in: - a) cubic meters, - b) cubic kilometers, and - c) gallons.2. **Speed Comparison of Animal and Fish** - The fastest land animal is the cheetah, reaching speeds of up to 70 mph (miles per hour). The fastest fish, the sailfish, swims at 30.5 m/s (meters per second). Which one is faster? Perform conversions by hand and show all work.3. **Molecular and Ocean Mass Calculations** - An atom of oxygen has a mass of 16 u (atomic mass unit), and an atom of hydrogen has a mass of 1 u. - a) What is the mass of a water molecule (\(H_2O\)) in kg? - b) The mass of water in the Earth’s oceans is about \(1.2 \times 10^{21} \, \text{kg}\). How many molecules of water make up this mass?4. **Paint Coverage Calculation** - A can of paint claims to cover an area of 400 ft\(^2\) per gallon. - a) Express this quantity in square meters per liter. - b) Express this quantity in SI base units. - c) Consider the inverse of the original quantity. What is the physical meaning of this new quantity?5. **Pendulum Clock Time Correction** - A pendulum clock with a 12-hour dial gains 2.0 minutes per day. After setting the clock to the correct time, how long will it take for the clock to read the exact correct time again?6. **Unit Conversion** - Convert the following measurements to the units indicated: - a) 34 nm → cm - b) 0.0136 m/s → μm/min - c) 9.3 m\(^2\) → mm\(^2\) - d) 98 cm\(^2\) → km

Given: Depth of dig = 15 m. Area of digging = 3 hectare = 3×104 m2

1. One hectare, a unit of measure often used in measuring land areas, is defined to be 10 m2. In an effort to dig to China, a desperate grad student digs a pit 15 m deep over an area of 3 hectares before he happily dies of exhaustion. What volume of earth has he managed to exhume? Express your answer in: a) cubic meters, b) cubic kilometers, and c) gallons.

1. One hectare, a unit of measure often used in measuring land areas, is defined to be 10 m2. In an effort to dig to China, a desperate grad student digs a pit 15 m deep over an area of 3 hectares before he happily dies of exhaustion. What volume of earth has he managed to exhume? Express your answer in: a) cubic meters, b) cubic kilometers, and c) gallons.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Please solve 1 and 3

### Educational Website Transcription

#### Problems Set

1. **Land Excavation Calculation**
- One hectare, a unit of measure often used in measuring land areas, is defined to be \(10^4 \, \text{m}^2\). A student in China excavates a pit 15 m deep over an area of 3 hectares. How much earth does he manage to exhume? Express your answer in:
- a) cubic meters,
- b) cubic kilometers, and
- c) gallons.

2. **Speed Comparison of Animal and Fish**
- The fastest land animal is the cheetah, reaching speeds of up to 70 mph (miles per hour). The fastest fish, the sailfish, swims at 30.5 m/s (meters per second). Which one is faster? Perform conversions by hand and show all work.

3. **Molecular and Ocean Mass Calculations**
- An atom of oxygen has a mass of 16 u (atomic mass unit), and an atom of hydrogen has a mass of 1 u.
- a) What is the mass of a water molecule (\(H_2O\)) in kg?
- b) The mass of water in the Earth’s oceans is about \(1.2 \times 10^{21} \, \text{kg}\). How many molecules of water make up this mass?

4. **Paint Coverage Calculation**
- A can of paint claims to cover an area of 400 ft\(^2\) per gallon.
- a) Express this quantity in square meters per liter.
- b) Express this quantity in SI base units.
- c) Consider the inverse of the original quantity. What is the physical meaning of this new quantity?

5. **Pendulum Clock Time Correction**
- A pendulum clock with a 12-hour dial gains 2.0 minutes per day. After setting the clock to the correct time, how long will it take for the clock to read the exact correct time again?

6. **Unit Conversion**
- Convert the following measurements to the units indicated:
- a) 34 nm → cm
- b) 0.0136 m/s → μm/min
- c) 9.3 m\(^2\) → mm\(^2\)
- d) 98 cm\(^2\) → km

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