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:

1. What type of function does each trajectory describe?
2. At which points do their trajectories coincide?
3. 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.