Activity

Studying Trajectories at NASA

Characters:

Katherine Johnson (The human calculator)

Theme: Relationships and functions

Competencies

Mathematical competence in science, technology and engineering

Digital Competence

Personal, social and learning to learn competence

Competence in cultural awareness and expressions

Subjects and year by Educational System

Spain > Mathematics > 2nd ESO > Algebraic sense

Spain > Mathematics > 2nd ESO > Socio-affective sense

Enunciation

<img title="Women's Legacy logo" src="//inclusion.womenslegacyproject.eu/images/LogoWL.svg" /><hr /><img title="Katherine Johnson's Portrait" src="//inclusion.womenslegacyproject.eu/uploads/resume/attachment/2720/Katherine_Johnson.png" alt="Katherine Johnson's Portrait" width="100" height="131" />
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.
<img title="Rocket and Aircraft trajectories" src="//inclusion.womenslegacyproject.eu/uploads/resume/attachment/2722/Projectile_and_Aircraft_trajectories.png" alt="Rocket and Aircraft trajectories" width="400" height="337" />
1- Take a look at the graph and answer the following questions:
<ol style="list-style-type: lower-alpha;">
<li>What type of function represents the trajectory of the plane? And the projectile's trajectory?</li>
<li>What is the maximum height that the projectile reaches? What distance does it land in?</li>
<li>At which points do the two trajectories coincide?</li>
</ol>
2. &nbsp; Observe three planes in the sky, the trajectories they follow are linear functions. The plane to Barcelona follows the function f(x) = 3x + 1, while the plane to Budapest is g(x) = x + 2, and the one to Cairo is h(x) = -x + 6. Draw a graph in an axis of coordinates of the three trajectories and find the points that they coincide in.

Observations and context

- 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, visualise trajectories and delve into how each parameter changes the graphs and, therefore, conditions them.

- This activity can also be done in physics and chemistry.

- It is recommended to use GeoGebra to show the results, visualise trajectories and delving into how each parameter changes the graphs and, therefore, conditions them.

- 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.

Description

We will study the graphic of a trajectory by analysing some of its characteristics.

Studying Trajectories at NASA

Enunciation

Observations and context

Description

Answer

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