Companion to the reading passage The Physics of the Plunge: Force, Acceleration, and Terminal Velocity. Answer each question, then click Check. Multiple-choice and number questions grade themselves; for written answers, compare yours with the model answer and checklist, then score yourself honestly.
A skydiver and her gear have a total mass of 80.0 kilograms. She steps out of an airplane about 3,000 meters above the ground. As her speed increases, the upward force of air resistance (drag) on her increases, while the downward gravitational force on her stays the same. Eventually she falls at a constant speed called terminal velocity. Later she opens her parachute, which greatly increases the area that pushes against the air.
Picture the skydiver as a dot, one second after her parachute fully opens. A downward arrow 2 centimeters long represents the gravitational force on her.
1. The skydiver is represented as a dot, one second after her parachute fully opens. A downward arrow 2 centimeters long represents the gravitational force on her. Which arrow, drawn starting at the dot, best represents the force of air resistance on her at this instant? (Use the 2-cm arrow as a scale.)
An altimeter worn by the skydiver recorded her downward speed during the first 14 seconds of the jump, before she opened her parachute. The results are shown in Table 1.
Table 1: Skydiver’s Speed During Free Fall
| Time (s) | Downward Speed (m/s) |
|---|---|
| 0 | 0.0 |
| 2 | 18.8 |
| 4 | 33.5 |
| 6 | 42.9 |
| 8 | 48.2 |
| 10 | 50.9 |
| 14 | 53.0 |
Data are representative values for practice.
2. Which graph best represents the skydiver’s speed as a function of time for the data in Table 1?
3. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
Engineers dropped three objects from the same height in a tall testing tower and measured the terminal velocity of each. Objects A and B are spheres of the same size and shape, but B has twice the mass. Object C has the same mass as A but carries a small parachute that increases its cross-sectional area.
Table 2: Tower Drop Results
| Object | Mass (kg) | Cross-Sectional Area (m2) | Terminal Velocity (m/s) |
|---|---|---|---|
| A: Standard sphere | 5.0 | 0.05 | 45 |
| B: Weighted sphere | 10.0 | 0.05 | 64 |
| C: Sphere with parachute | 5.0 | 0.85 | 11 |
Data are representative values for practice.
4. Substitute numerical values into a mathematical representation that can be used to determine the magnitude of the air resistance force on Object B while it falls at terminal velocity. Then calculate the force.
5. Which row correctly compares Object B with Object A when each is falling at its terminal velocity? (Columns: air resistance force on B compared with A / net force on B.)
NASA engineers are designing a parachute for a robotic rover that will land on Mars. The acceleration due to gravity on Mars is about 3.7 m/s2, and the density of the Martian atmosphere is less than 1% of the density of Earth’s atmosphere near the ground. A parachute design that gives a gentle landing on Earth would produce far less air resistance at the same speed on Mars. The landing system must also fit inside a spacecraft with limited mass and volume.
6. Describe one change the engineers could make to the parachute or landing system to reduce the rover’s landing speed on Mars, and identify one constraint or trade-off that this change creates.