Trajectory of a projectile at NASA
Characters:
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 > 1st ESO > Algebraic sense
Spain > Mathematics > 1st ESO > Socio-affective sense
Enunciation
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 a similar way as we are going to do now.
1. In the picture above, we can see a graph for a projectile trajectory. The vertical axis represents the height that it reaches above ground level, while the horizontal axis represents the distance from the take-off point. Take a look at the graph and answer the following questions:
- What is the maximum height that the projectile reaches?
- What distance is it from the take-off point?
- At what distance does the projectile land in?
2. The trajectory of a plane and a projectile are represented in the following figure. In which points do the two trajectories coincide?
Observations and context
This activity belongs within the topic of functions, 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.
This activity can also be done in physics and chemistry.
A life that was brought to the big screen
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.
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, Vivienne Malone, Martha Jane Bergin Thomas, Rosalind Franklin, Jocelyn Bell, Vera Rubin, Mileva Maric, or Hilda Geiringer.
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.
Description
We will study the graphic of a trajectory by analysing its characteristics.