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:

1. What is the maximum height that the projectile reaches?
2. What distance is it from the take-off point?
3. 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?