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Velocity, distance and time

Problem 1:Generally, we know the equation for velocity (a rate) to be:

Where v = velocity, d = distance and t = time.

This equation can be rearranged so that you have an

equation for distance (d) and time (t).

1. Rearrange the velocity equation to create an equation for distance (d).

2. Rearrange the velocity equation to create an equation for time (t).

Use the equations that you manipulated above to solve the following problems:

Problem 2: A wave traveling downward

from the surface of the ocean at 1.5 km/sec

takes six seconds to reflect off the ocean

floor. How deep is the ocean at that site?

Problem 3: Imagine that you are working

with Ms. Homeowner to understand the

groundwater flow in her area. She is

particularly interested in an underground tank that is located 2.6 km from her home. You have

measured the velocity of the groundwater to be 0.033 km/day. About how long will it take any

contaminants leaking from the tank to reach Ms. Homeowner's well?

Density

Density plays an important role in our understanding of the physical properties of Earth

materials. The equation for density is similar to that for velocity and, as such, it can be

manipulated so that you can solve for any of the variables involved. The next few problems

utilize the equation for density:

which can be shortened to:

Problem 1: Manipulate (rearrange) the density equation (above) to create an equation for mass.

Problem 2:Manipulate the density equation to create an equation for volume.

Use the equations that you manipulated above to solve the following problems:

Problem 3:Continental crust has a density of about 2.75 g/cm3. What volume would 1000 g (1

kg) of continental crust occupy?

Problem 4:The outer core has a density of about 10.5 g/cm3. What volume would 1000 g (1 kg)

of the outer core occupy?

Isostasy

Isostasy is an important concept in the geosciences

that is related to density. The concept of isostasy

explains why continental crust sits so much higher

than oceanic crust. It involves properties of an

object like height and density. It also explains why

only a portion of an iceberg is visible above water.

The following problems involve an equation that is

important to understanding the way that continental

crust/oceanic crust behave on the Earth. If you need

help visualizing the problem, click on the

illustration below to see a larger version.

The equation for calculating the height of an object above the "fluid" in which it is floating is:

where:

Htotal = total height of the object

object = density of the object of interest (e.g., iceberg, continental crust, etc.)

fluid = density of the fluid in which the object is floating (e.g., seawater, mantle, etc.)

Habove = height of the object visible above the fluid.

Problem 1: Rearrange the equation above to solve for Htotal.

Problem 2: Use the equation that you generated in Problem 1 to calculate the thickness

(Htotal) of continental crust if:

? the density of continental crust (object) is 2.79 g/cm3,

? the density of the mantle (fluid) is 3.3 g/cm3,

? and, the average height of the continents above the mantle is 4.5 km (Habove).

Problem 3: Use the information from Problem 2 to calculate the thickness of crust that lies

below the mantle (e.g., Hbelow).

What is the equation used to calculate distance? To calculate the 2-D distance between these two points, follow these steps: Input the values into the formula: √ [ (x₂ - x₁)² + (y₂ - y₁)²]. Subtract the values in the parentheses. Square both quantities in the parentheses. Add the results. Take the square root. Use the distance calculator to check your results.

Title: Microsoft Word - Rearranging equations

Author: ebaer

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