Aircraft trajectories
Personajes:
Tema: Relationships and functions
Competencias
Competencia Matemática, en ciencia, tecnología e ingeniería
Competencia Digital
Competencia Personal, social y de aprender a aprender
Competencia en conciencia y expresiones culturales
Materias y cursos por Sistema Educativo
España > Matemáticas > 3º ESO > Sentido algebraico
España > Matemáticas > 3º ESO > Sentido socioafectivo
Enunciado
Katherine Johnson (1918-2020) was a mathematician of African descent who worked during the 1950s and 1960s in the calculations of trajectories for NACA (currently known as NASA) missions. She used functions to mathematically represent trajectories.
In the following picture, the trajectories of a projectile and a plane are represented.
1- Take a look at the graph and answer the following questions:
- What type of function does each trajectory describe?
- At which points do their trajectories coincide?
- Find the equations to the plane's trajectory using the graph.
2- The trajectories of two planes can be described using linear functions, like in the activity 1 of this activity. Find the expression of the trajectory of a plane to Barcelona given the fact that the slope is m=3, and the trajectory of a plane to Budapest with slope m=2. Keep in mind that they meet at (1,4).
3- EXTENSION ACTIVITY: Find the equation for the trajectory of the projectile of activity 1 using the graph.
Observaciones y contexto
- This activity belongs within the topic of functions in mathematics, giving context for one of its most popular applications.
- It is recommended to use GeoGebra to show the results, visualize trajectories and delve into how each parameter changes the graphs and, therefore, conditions them.
- The extension activity is more difficult because they have to find the expression for a parabola from two of the points of the graph. It is recommended to do it as an extension activity or to improve the curriculum.
- This activity can also be done in physics and chemistry.
- Her work is a continuation of that of a long list of women who have dedicated their lives to calculating the trajectories of stars, such as Hypatia (c.370-c.416), Sophia Brahe (1556-1643), Maria Cunitz (1610-1664), Nicole Lepaute (1723-1788), Caroline Herschel (1750-1848), an astronomer who discovered eight comets, and Henrietta Swan Leavitt (1868-1921) an American astronomer. They have collected their current scientific witness as Maria Assumpció Català i Poch (1925-2009), Antonia Ferrín Moreira (1914-2009) or Francesca Figueras (1958).
- She was a contemporary of mathematicians and scientists such as Maria Goeppert Mayer (1906-1972), Vivienne Malone (1932-1995), Martha Jane Bergin Thomas (1926-2006), Rosalind Franklin (1920-1958), Jocelyn Bell (1943), Vera Rubin (1928-2016), Mileva Maric (1875-1948), or Hilda Geiringer (1893-1973).
- As an Afro-descendant woman in the context of racial segregation, her access to studies and later work was more complicated. This story is common to other black women, who had to break many barriers. An example of them was Angie Turner King, Katherine Johnson's teacher and one of the first women to obtain degrees in chemistry and mathematics. Katherine worked hand in hand with great scientists such as Dorothy Johnson Vaughan. In 1973, in Massachusetts, physicist Shirley Ann Jackson became the first African-American woman to earn a Ph. D. from MIT.
- In 2016, the film Hidden Figures was released, a film that tells the story of Katherine Johnson and her two colleagues, Dorothy Vaughan and Mary Jackson, who while working in the Segregated Computing Division of the West Wing of the Langley Research Center, helped NASA in the Space Race.
Descripción
We will study different trajectories through their graphs and analysing their characteristics.