Question 1: Define terminal velocity and explain the scientific principles behind it.

Answer: Terminal velocity is the constant speed that a freely falling object reaches when the force of gravity is balanced by the air resistance or drag acting opposite to its motion. It occurs when the net acceleration becomes zero, and the object continues to fall at this steady speed.

Question 1: List two factors that influence the terminal velocity of an object falling through the air.

Answer: The mass of the object and the surface area facing the direction of motion are two factors that influence terminal velocity.

Question 2: Describe how increasing the surface area of an object affects its terminal velocity.

Answer: Increasing the surface area increases air resistance, which can reduce the terminal velocity, making the object fall more slowly once terminal velocity is reached.

Question 1: A skydiver with a mass of 80 kg jumps from a plane. If the air resistance balances gravity at a speed of 55 m/s, what is the magnitude of the air resistance force at terminal velocity? (Use F = m * g).

Answer: F = 80 kg * 9.8 m/s² = 784 N

Question 2: An aluminum ball with a surface area of 0.02 m² and a mass of 0.5 kg reaches a terminal velocity of 15 m/s. If the air density is 1.2 kg/m³ and the drag coefficient is 0.5, verify the terminal velocity using the drag force formula: F_d = 0.5 * air_density * v² * drag_coefficient * area.

Answer: F_d = 0.5 * 1.2 * (15)² * 0.5 * 0.02 = 0.5 * 1.2 * 225 * 0.5 * 0.02 = 0.5 * 1.2 * 225 * 0.01 = 1.35 N. Since F_d balances weight (0.5 kg * 9.8 m/s² = 4.9 N), the actual terminal velocity is consistent with these values.

Question 1: Design a simple experiment to measure the terminal velocity of a small ball bearing falling through air. List the variables you would control and measure, and mention safety precautions.

Answer: The experiment involves dropping a small ball bearing from a fixed height in a controlled environment, using a stopwatch to measure the time taken to reach terminal velocity. Variables to control include the height of drop, air currents, and ball material. Variables to measure include fall time and final speed. Safety precautions include ensuring the drop area is clear of obstacles and wearing eye protection if necessary.

Question 1: A drone designed to deliver packages is tested for its maximum safe descent speed. The engineers observe that when the drone descends at 8 m/s, the air resistance equals the weight of the drone. If the drone's mass is 2 kg, what is the magnitude of the air resistance force at this speed? What assumptions are made in this scenario?

Answer: The air resistance force is equal to the weight: F = m * g = 2 kg * 9.8 m/s² = 19.6 N. Assumptions include that the drone is in steady descent, and air resistance is the only horizontal force balancing gravity.

Question 1: Explain how understanding terminal velocity can help engineers design safer parachutes or falling objects.

Answer: Engineers use knowledge of terminal velocity to design parachutes that increase air resistance, thereby reducing the falling speed of objects or people to ensure safe landing speeds.