Question

1. sketch a graph of the following scenario. label the axes and identify any maximum or minimum values. a skydiver steps out of a plane. his speed increases due to gravity until he reaches terminal velocity of 40 meters per second after falling for about 25 seconds. his speed remains at terminal velocity for 5 seconds. then he pulls the cord to release his parachute and his speed is rapidly reduced to about 12 meters per second. his speed then decreases to 5 meters per second and remains constant as he moves toward the ground. he reaches the ground about 55 seconds after he stepped out of the plane.

Explanation:

Step1: Define the x - axis and y - axis

Let the x - axis represent time (in seconds) and the y - axis represent speed (in meters per second).

Step2: Analyze the first phase

From \(t = 0\) to \(t=25\) seconds, the speed \(v\) increases from \(0\) to \(40\) m/s. This is a non - linear (due to acceleration from gravity) increasing curve on the graph.

Step3: Analyze the second phase

From \(t = 25\) to \(t = 30\) seconds, the speed \(v = 40\) m/s. So, it is a horizontal line at \(y = 40\) on the graph.

Step4: Analyze the third phase

When the parachute is deployed (at \(t = 30\) seconds), the speed rapidly drops from \(40\) m/s to about \(12\) m/s. This is a steep downward - sloping line on the graph.

Step5: Analyze the fourth phase

From the point where the speed is \(12\) m/s, it decreases to \(5\) m/s. This is a downward - sloping line.

Step6: Analyze the fifth phase

From the point where the speed reaches \(5\) m/s until \(t = 55\) seconds, the speed \(v = 5\) m/s. So, it is a horizontal line at \(y = 5\) on the graph.
The maximum speed is \(40\) m/s which occurs from \(t = 25\) to \(t = 30\) seconds. There is no minimum speed in the traditional sense as the speed starts from \(0\) and then stabilizes at \(5\) m/s at the end.

Answer:

The graph has time on the x - axis and speed on the y - axis. It has an increasing curve from \(t = 0\) to \(t = 25\) s, a horizontal line from \(t = 25\) to \(t = 30\) s at \(y = 40\), a steep downward - sloping line from \(t = 30\) s when the parachute is deployed to a lower speed, then a downward - sloping line to reach \(y = 5\) and then a horizontal line at \(y = 5\) until \(t = 55\) s. The maximum speed is \(40\) m/s.