Question
A plane moving at a rate of 345 km.h north has a different
plane moving 345 km/h northwest.
than a
Newton
Velocity
Rate
Speed
plane moving 345 km/h northwest.
than a
Newton
Velocity
Rate
Speed
Answers
GPT-4o mini
In the context of physics and specifically Newtonian mechanics, the two planes you mentioned are moving at the same speed (345 km/h), but their velocities are different because velocity is a vector quantity that includes both speed and direction.
1. **Speed**: This is a scalar quantity that refers only to how fast an object is moving, regardless of its direction. In this case, both planes have a speed of 345 km/h.
2. **Velocity**: This is a vector quantity that includes both the speed and direction of motion.
- The first plane is moving **north** at a velocity of 345 km/h north.
- The second plane is moving **northwest**, which is typically defined as 45 degrees between north and west. To describe its velocity vector mathematically, you can break it down into its components:
- North component: \( 345 \times \cos(45^\circ) = 345 \times \frac{\sqrt{2}}{2} \approx 243.59 \) km/h north
- West component: \( 345 \times \sin(45^\circ) = 345 \times \frac{\sqrt{2}}{2} \approx 243.59 \) km/h west
The key takeaway is that although both planes have the same speed, their velocities are different due to the difference in direction.
- The first plane has a velocity of **345 km/h north**.
- The second plane has a velocity of approximately **243.59 km/h north and 243.59 km/h west** (or simply **345 km/h northwest**).
1. **Speed**: This is a scalar quantity that refers only to how fast an object is moving, regardless of its direction. In this case, both planes have a speed of 345 km/h.
2. **Velocity**: This is a vector quantity that includes both the speed and direction of motion.
- The first plane is moving **north** at a velocity of 345 km/h north.
- The second plane is moving **northwest**, which is typically defined as 45 degrees between north and west. To describe its velocity vector mathematically, you can break it down into its components:
- North component: \( 345 \times \cos(45^\circ) = 345 \times \frac{\sqrt{2}}{2} \approx 243.59 \) km/h north
- West component: \( 345 \times \sin(45^\circ) = 345 \times \frac{\sqrt{2}}{2} \approx 243.59 \) km/h west
The key takeaway is that although both planes have the same speed, their velocities are different due to the difference in direction.
- The first plane has a velocity of **345 km/h north**.
- The second plane has a velocity of approximately **243.59 km/h north and 243.59 km/h west** (or simply **345 km/h northwest**).