Applications with Radical Equations
Learning Outcome
- Solve application problems involving kinetic energy, volume, and free-fall
Kinetic Energy
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Example
What is the kinetic energy of an object with a mass of kilograms that is traveling at meters per second?Answer: Identify variables and known values.
Substitute values into the formula.
Solve the radical equation for Ek.
Now check the solution by substituting it into the original equation.
The Kinetic Energy is Joules.
Volume
Harvester ants found in the southwest of the U.S. create a vast interlocking network of tunnels for their nests. As a result of all this excavation, a very common above-ground hallmark of a harvester ant nest is a conical mound of small gravel or sand [footnote]Taber, Stephen Welton. The World of the Harvester Ants. College Station: Texas A & M University Press, .[/footnote]
Example
A mound of gravel is in the shape of a cone with the height equal to twice the radius. Calculate the volume of such a mound of gravel whose radius is ft. Use .Answer: The radius of a cone given its volume can be found with the following formula: , Cube both sides to eliminate the cube root.
Therefore, the volume is about 100 cubic feet.
Free-Fall
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Example
Find the time it takes to reach a height of 400 feet by first finding an expression for t.Answer: We are asked two things. First, we will solve the height equation for t, then we will find how long it takes for the object's height above the ground to be 400 feet. Solve for t: At this point, let us stop and talk about whether it makes sense to include both . We want time to be only positive since we are talking about a measurable quantity, so we will restrict our answers to just . We want to know at what time the height will be 400 ft., so let us substitute 400 for h. It takes seconds for the object to be at a height of ft.