Question 1: Terminal velocity is the constant speed that a freely falling object reaches when the force of gravity is balanced by the air resistance. Explain in your own words how this balance affects the motion of the object.

Answer: When the force of gravity pulling the object downward equals the upward force of air resistance, the object stops accelerating and continues falling at a constant speed called terminal velocity.

Question 1: What are the main forces acting on a falling object that determines its terminal velocity?

Answer: Gravity (weight) and air resistance (drag).

Question 2: Describe how the shape and mass of an object influence its terminal velocity.

Answer: A streamlined shape reduces air resistance, increasing terminal velocity, while a heavier mass increases gravitational force, also raising terminal velocity.

Question 1: A skydiver with a mass of 80 kg jumps from a plane. Assuming the drag coefficient and cross-sectional area result in a drag force that balances gravity at a speed of 55 m/s, verify if this is the terminal velocity. (Use g = 9.8 m/s²)

Answer: Yes, the given speed is the terminal velocity as it is the speed at which the forces balance; calculations confirm that at 55 m/s, air resistance equals weight.

Question 2: Calculate the approximate terminal velocity of a raindrop with a mass of 0.02 grams (0.00002 kg), a drag coefficient of 0.5, a cross-sectional area of 1 x 10^-6 m², and air density of 1.2 kg/m³. Use the formula: v = √(2mg / (ρACd)).

Answer: v ≈ 9.8 m/s

Question 1: Design a simple experiment (theory only) to demonstrate how the size of an object affects its terminal velocity. Include the variables you would change and safety precautions.

Answer: Possible response: Use objects of different sizes but similar shapes (e.g., small and large balls). Drop them from a fixed height in a safe environment, such as a tall open space. Variables: size of object, shape, mass. Safety precautions: ensure the drop zone is clear, use safety gear if needed, and do not drop objects from heights that could cause injury.

Question 1: A drone with a mass of 2 kg is designed to reach a maximum speed of 15 m/s when falling. If the drone’s shape is modified to be more aerodynamic, explain how this could affect its terminal velocity and why.

Answer: Making the drone more aerodynamic reduces air resistance, which can increase its terminal velocity, allowing it to fall faster before reaching the balance of forces.

Question 1: Explain how understanding terminal velocity is important in designing parachutes for skydivers.

Answer: Designers aim to increase air resistance to reduce terminal velocity, allowing skydivers to land safely by slowing their descent.

Question 2: Identify a technological application where controlling terminal velocity is crucial, and briefly describe its significance.

Answer: In space capsule re-entry, controlling terminal velocity ensures a safe descent through the atmosphere, preventing excessive heat and impact forces.