Elite Extension: The Ares-V Martian Descent

Subject: Science | Year: 5

Name: _________________________ Class/Set: ____________ Date: _________

TEACHER GUIDE: Facilitation & Support

High-ability learners in the top 10% often master the concept of 'gravity' as a static downward pull very quickly. To prevent cognitive stagnation, this task introduces the concept of Fluid Resistance and Terminal Velocity (Year 7/8 concepts) through the lens of a multi-variable optimisation problem. This moves the student from simple observation to systemic analysis, requiring them to balance mass against surface area to achieve a specific outcome in a simulated low-density environment.

How to guide the student:

• Stimulus: Ask: "If you were on the Moon, where there is no air, would a hammer and a feather land at the same time? Why is it different on Earth or Mars?"
• Unblocking: If the student is stuck on the 'Descent Paradox', ask them to calculate the 'Surface Area per Gram' (cm²/g) for each pod. This helps them see the relationship between the variables.
• Observation: Watch for students who realise that as the mass increases, the air resistance must increase proportionally to maintain the same descent speed.

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The Mission

You are the Lead Aeronautical Engineer for the Ares-V Colony on Mars. A critical shipment of medical supplies and heavy machinery is currently in orbit. Because the Martian atmosphere is 100 times thinner than Earth’s, your "Drop-Pods" are at risk of smashing into the surface. You must design a parachute system that ensures both the 'Light Medical Kit' and the 'Heavy Drill' land at the exact same velocity (speed) to ensure the recovery team can reach them at a single landing site.

The Challenge

Task: "The Descent Optimisation Investigation"

You are provided with two Supply Pods with different masses. Your goal is to determine the required parachute surface area for the Heavy Pod so that it falls at the same rate as the Light Pod.

The Data Constraints:

• Gravity (Mars): 3.7 m/s² (pulls the pods down).
• Atmospheric Resistance: Pushes up against the surface area of the parachute.
• The Light Pod: Mass = 200g | Parachute Surface Area = 400cm².
• The Heavy Pod: Mass = 800g | Parachute Surface Area = ?

Instructions:

1. Calculate the Ratio: Determine the 'Surface Area per Gram' for the Light Pod. (Formula: Area ÷ Mass).
2. Predict: If the Heavy Pod is 4 times heavier, will a parachute that is 4 times larger (1,600cm²) result in the same speed? Or will the increased momentum require a different scale?
3. Variable Analysis: Complete the 'Martian Physics Table' below to test your hypothesis.
4. The Conclusion: Write a brief report to the Ares-V Commander explaining why the relationship between mass and air resistance is not always a simple 1:1 scale in high-velocity descents.

Success Criteria:

• Accurate calculation of the cm²/g ratio for both pods.
• A completed data table showing the relationship between Mass, Area, and Resistance.
• A professional explanation using the terms: Gravity, Air Resistance, Equilibrium, and Mass.

The Martian Physics Table

Payload Item	Mass (g)	Surface Area (cm²)	Ratio (cm²/g)	Predicted Speed
Light Medical Kit	200g	400cm²		Constant (Target)
Heavy Power Drill	800g			Constant (Target)
Emergency Rover	2,000g			Constant (Target)

Hint / Starting Point

In a vacuum, everything falls at the same rate. On Mars, we have a little bit of air. To keep the speed the same, the 'Upward Push' (Air Resistance) must balance the 'Downward Pull' (Weight). If you have 4 times the mass pulling down, you generally need 4 times the resistance pushing up. Start by checking if your cm²/g ratio remains the same for all payloads.

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⚠ TEACHER’S GUIDANCE

The Solution:

• Task 1 (Ratio): The Light Pod ratio is 2 cm²/g (400 ÷ 200).
• Task 2 (Heavy Pod Area): To maintain the same speed, the Heavy Pod requires 1,600cm² (800 × 2).
• Task 3 (Emergency Rover Area): The Rover requires 4,000cm² (2,000 × 2).

Cognitive Pathway Analysis:

• Approach A (Procedural): The student correctly identifies the 1:1 linear relationship and multiplies the area by the same factor as the mass. They demonstrate strong functional numeracy.
• Approach B (Scientific Modeller): The student questions if the ratio stays exactly the same in a thinner atmosphere. They may suggest that "Terminal Velocity" might be reached faster or slower depending on the shape, not just the area.
• Approach C (Elite Analyst): The student identifies that while the math is linear here, in reality, air resistance increases with the square of the velocity. They may note that Mars' low gravity (3.7 m/s²) means the 'Downward Pull' is weaker than on Earth, requiring different calculations for an Earth-based drop.

Background & Theoretical Synthesis:

• The Theory: Terminal Velocity and Equilibrium. When the force of gravity (weight) and the force of air resistance (drag) are equal and opposite, the object stops accelerating and falls at a constant speed.
• Mentorship Talk (10-15 mins):
  1. The Misconception: Ask: "Why do people think heavy things fall faster?" (Address the confusion between Force and Acceleration).
  2. The Variable Twist: "If we doubled the speed of the fall, would we only need double the parachute? (No, air resistance increases exponentially with speed—this is why streamlining matters in F1 cars)."
  3. The Martian Context: Discuss how the thin air on Mars makes parachutes less effective, requiring 'Retro-rockets' or 'Airbags' for the final landing.
• Real-World Impact: This logic is used by SpaceX when landing the Falcon 9 boosters and by NASA engineers when designing the 'Sky Crane' for the Perseverance Rover.

Diagnostic Quiz (Check for Mastery):

1) Which force is responsible for pulling the Ares-V Pods towards the Martian surface?

• a) ☐ Upthrust
• b) ☐ Magnetism
• c) ☐ Gravity
• d) ☐ Friction

Answer 1: c) ☐ Gravity.

2) If an engineer increases the Surface Area of a parachute, what happens to the Air Resistance?

• a) ☐ It stays the same.
• b) ☐ It increases.
• c) ☐ It decreases.
• d) ☐ It disappears.

Answer 2: b) ☐ It increases (more air molecules hitting the fabric).