Question 1: Define scalar and vector quantities and give two examples of each.

Answer: A scalar quantity has magnitude only, such as mass or temperature. A vector quantity has both magnitude and direction, such as force or velocity.

Question 1: Explain why velocity is considered a vector quantity while speed is a scalar.

Answer: Velocity is a vector because it includes both magnitude and direction, whereas speed only measures magnitude without direction.

Question 2: Describe how vector addition differs from scalar addition.

Answer: Vector addition considers both magnitude and direction, often requiring methods like tip-to-tail, whereas scalar addition sums only magnitudes without regard to direction.

Question 1: A car travels north at 60 km/h for 2 hours. Calculate the total distance travelled and state whether this is a scalar or vector quantity.

Answer: Distance = speed × time = 60 km/h × 2 h = 120 km. It is a scalar quantity.

Question 2: Two forces of 10 N east and 15 N north act on an object. Calculate the resultant force magnitude.

Answer: Resultant force = √(10² + 15²) = √(100 + 225) = √325 ≈ 18.03 N.

Question 1: Describe a simple experiment to demonstrate the difference between scalar and vector quantities involving a force meter.

Answer: Attach a force meter to an object and measure the force in different directions. Record the magnitude alone (scalar) and the magnitude with direction (vector). Ensure the object is on a smooth surface to avoid additional forces.

Question 2: List three safety precautions when conducting experiments involving forces.

Answer: Use appropriate protective equipment, ensure objects are securely fixed, and avoid overloading equipment to prevent accidents.

Question 1: A cyclist travels 30 km east, then 40 km south. Calculate the magnitude of their resultant displacement and describe the direction relative to east.

Answer: Displacement = √(30² + 40²) = √(900 + 1600) = √2500 = 50 km. The direction is approximately south-east.

Question 2: A boat moves with a velocity of 5 m/s due west. If the wind exerts a force in the opposite direction at 2 N, discuss how the vector nature of force affects the boat’s motion.

Answer: Since velocity is a vector, its direction west combined with the opposing force (also a vector) affects the net force and overall motion. The force in the opposite direction reduces the boat’s effective velocity, demonstrating how vector quantities combine to influence motion.

Question 1: Explain how the concept of vectors is essential in the design of modern navigation systems such as GPS.

Answer: GPS relies on vector calculations of positions, velocities, and directions to accurately determine a location and guide movement, demonstrating the importance of vector quantities.

Question 2: Describe a real-world scenario where misunderstanding scalar and vector quantities could lead to a significant error in measurement or safety.

Answer: In aviation, confusing scalar speed with velocity can lead to navigation errors, especially when considering wind direction and speed. Misinterpreting these vector quantities could result in incorrect course adjustments, risking safety.