Single Variable Calculus, Chapter 1, 1.1, Section 1.1, Problem 18

Express the horizontal distance x traveled by the airplane and its altitude y as a function of time in minutes when an airplane takes off from an airport and lands an hour later at another airport, 400 miles away.



a.) Sketch a graph of horizontal distance x as a function of time








The figure shows that the horizontal velocity of the air plane is constant except at the take off and landing.




b.) Sketch a graph of altitude y as a function of time









Let's say that the height where the air plane become steady after take off is 20,000 feet and it will remain the same altitude throughout the journey except for the take off and landing.




c.) Sketch a possible graph of the ground speed









The ground speed is the horizontal velocity that indicates the speed of the air plane relative to the ground. Just like the graph in part \textbf{(a)} the horizontal velocity is constant except for take off and landing.




d.) Sketch a possible graph of the vertical velocity








Velocity is a vector quantity , it depends on the direction and it can be either positive or negative. The vertical velocity of the plane during take off is positive and increasing because the plane is ascending. As the plane becomes steady or it already reacted its cruising height, the vertical velocity decreases to zero and it remains zero during the entire duration where the plane is steady. As the plane is landing, its vertical velocity become negative and opposite as it was during take off.