Shot in the dark
Introduction-
Shot in the Dark is an applied problem assigned as part of our first semester exam. The problem required us to look at the trajectory traveled buy a small ball thrown by a device. The balls position was recorded at intervals of .05 seconds and we were tasked with calculating its initial velocity, maximum height, acceleration, velocity from this data.
Analysis-
Justification-
In the problem there are three different types of functions: a position function, a velocity function, and an acceleration function, all of which relate to real life. This is why it is considered an applied problem. The ability to analyze, calculate, and determine their relationships by hand. I have learned a lot about how math not only fits into our academic lives but the real world. This is a great problem and showed me where I need to improve.
Shot in the Dark is an applied problem assigned as part of our first semester exam. The problem required us to look at the trajectory traveled buy a small ball thrown by a device. The balls position was recorded at intervals of .05 seconds and we were tasked with calculating its initial velocity, maximum height, acceleration, velocity from this data.
Analysis-
- Know and use a definition of a function to decide if a given relation is a function
- Perform algebraic operations on functions and apply transformations (translations, reflections, and rescaling)
- Explain how the rates of change of functions in different families (ex. Linear functions and quadratics) differ, referring to graphical representations
- Apply quadratic functions and their graphs in context of motion under gravity and simple optimization problems
- Find a quadratic function to model a given data set or situation
- Build quadratic models from verbal descriptions
- Know and use a definition of a function to decide if a given relation is a function
- Know and apply the definition and geometric interpretation of the difference quotient.
- Simplify difference quotients and interpret them as rates of change and slopes of secant lines.
- Perform algebraic operations (including compositions) on functions and apply transformations(translations, reflections and rescaling)
- Identify and describe discontinuities of a function (greatest integer function and Piecewise functions) and how these relate to the graph
- Assign independent and dependent variables be able to find minimum or maximum value in a real world problem
- Graphing Techniques: Transformation
- Translate written description of a real world problem into a mathematical model
Justification-
In the problem there are three different types of functions: a position function, a velocity function, and an acceleration function, all of which relate to real life. This is why it is considered an applied problem. The ability to analyze, calculate, and determine their relationships by hand. I have learned a lot about how math not only fits into our academic lives but the real world. This is a great problem and showed me where I need to improve.