Question

1. a kite starts on the ground and slowly ascends into the sky. it flies at the same altitude for about 10 minutes and then quickly drops to the ground. sketch a graph of the behavior of the kite over time.

Explanation:

Step1: Define axes

x-axis = Time, y-axis = Height (starts at (0,0))

Step2: Draw ascent segment

Shallow positive slope from (0,0) to point $(t_1, h)$ where $t_1>0, h>0$ (slow climb)

Step3: Draw level segment

Horizontal line from $(t_1, h)$ to $(t_1+10, h)$ (constant altitude for 10 mins)

Step4: Draw descent segment

Steep negative slope from $(t_1+10, h)$ to $(t_2, 0)$ where $t_2 - (t_1+10) < t_1$ (quick drop to ground)

Answer:

The graph has three distinct segments:

1. A shallow upward-sloping line starting at the origin (0,0), representing the kite's slow ascent to a constant height over time.
2. A horizontal line segment lasting 10 units of time on the x-axis, representing the kite staying at a fixed altitude.
3. A steep downward-sloping line from the end of the horizontal segment back to the x-axis (height = 0), representing the kite's quick descent to the ground.