A skydiver is 760 meters above the ground when he opens his parachute. After opening the parachute, he descends at a constant speed of 17 meter

Question

Part A: What type of function would best model this situation? Explain your answer.

Answer 1

To model the situation of a skydiver descending after opening their parachute, we can use a linear function. Here's why:

1. Constant Speed: After opening the parachute, the skydiver descends at a constant speed of 17 meters per second (m/s). This means that the vertical distance the skydiver falls varies linearly with time. The distance fallen in a given time can be expressed as:

   \[ \text{Distance} = \text{Rate} \times \text{Time} \]

   where the rate is 17 m/s.

2. Starting Point: The initial height when the parachute opens is 760 meters. Therefore, the relationship between height (h) above ground and time (t) can be expressed as:

   \[ h(t) = 760 - 17t \]

   This equation indicates that height decreases linearly over time, starting from 760 meters and decreasing at a constant rate.

Overall, the situation is best modeled by a linear function due to the constant rate of descent, resulting in a straight line when plotted on a graph. The height decreases steadily over time until the skydiver reaches the ground.