Which of the following quantities are vectors? Indude all that apply a distance traveled b displacement caverage speed d. average velocity e instantaneous velocity 2. Numerical values and directions are stated for a variety of quantities. Which of these statements represent a vector description? Indude all that apply. a 20 meters, west b. 9.8 m/s 35 ml/h, south d. 16 years old e 60 minutes 1 3.5 m/s/s, south 9:-3.5 misis +20 degrees 3. An airplane moves at 141 kryh toward the northeast (45 degrees). What is its component velocity in the northward direction? a. 41 km b. 100 110 km/h d. 141 km
The Correct Answer and Explanation is :
Answers:
- Which of the following quantities are vectors?
- b. Displacement
- d. Average velocity
- e. Instantaneous velocity Explanation:
A vector is a quantity that has both magnitude and direction. Let’s analyze each option: - Distance traveled (a): Scalar because it only has magnitude (total length of the path traveled).
- Displacement (b): Vector because it has both magnitude (how far) and direction (from start to finish).
- Average speed (c): Scalar because it only measures how fast an object moves, without considering direction.
- Average velocity (d): Vector because it considers both speed and direction.
- Instantaneous velocity (e): Vector because it represents the speed and direction of motion at a specific moment.
- Which of these statements represent a vector description?
- a. 20 meters, west
- c. 35 mi/h, south
- f. 3.5 m/s², south
- g. -3.5 m/s²
- h. +20 degrees Explanation:
A vector description includes both a magnitude (numerical value) and a direction. Let’s analyze each: - 20 meters, west (a): Has both magnitude and direction → Vector
- 9.8 m/s² (b): Only has magnitude, no direction → Scalar
- 35 mi/h, south (c): Includes both magnitude and direction → Vector
- 16 years old (d): Age has no direction → Scalar
- 60 minutes (e): Time has no direction → Scalar
- 3.5 m/s², south (f): Acceleration with direction → Vector
- -3.5 m/s² (g): Negative sign indicates direction → Vector
- +20 degrees (h): Angle indicates direction → Vector
- Airplane Velocity Component in the Northward Direction Given:
- Velocity = 141 km/h
- Direction = 45° (northeast)
- Northward component = V * sin(θ) Calculation:
[
V_y = 141 \times \sin(45^\circ)
]
[
V_y = 141 \times 0.707
]
[
V_y = 100 \text{ km/h}
] Final Answer:
b. 100 km/h Explanation:
When breaking a velocity vector into components, the northward component is given by V * sin(θ) and the eastward component is V * cos(θ). Since northeast means a 45-degree angle, both components are equal. Using trigonometry (sine function), we find that the northward velocity is 100 km/h.