12 m/s at 34° S of W
Well, that sounds like a fantastic speed and direction! With that kind of velocity, you'll be zooming in the southwest direction like a speedy squirrel on a mission. Just be careful not to go too fast and accidentally attract the attention of any cheetahs nearby. Trust me, they won't be able to resist chasing after someone so zippy!
To better understand the given information, let's break it down:
Magnitude: The magnitude of the velocity is given as 12 m/s. This tells us the speed of the object involved.
Direction: The direction is given as "34° S of W." We can interpret this as a clockwise angle of 34 degrees from the west direction, meaning it is pointing towards the southwest (or the south-southwest to be precise).
To visualize this direction, imagine a compass rose with north at the top. Draw a line from west towards the southwest, making an angle of 34 degrees with the west direction. This will give you the direction of the object.
So, in summary, the object is moving at a speed of 12 m/s towards the south-southwest direction, at an angle of 34 degrees from the west.
If you have any further questions, please let me know!
To break down the velocity of 12 m/s at 34° south of west, we can use vector components.
Step 1: Identify the given information:
- Magnitude of velocity: 12 m/s
- Direction of velocity: 34° south of west
Step 2: Convert the angle to its corresponding components:
To determine the components, we need to determine the horizontal and vertical directions using trigonometry.
- Horizontal component: We are facing west, so the x-component is negative.
horizontal component = magnitude of velocity * cos(angle)
horizontal component = 12 m/s * cos(34°)
horizontal component ≈ 12 m/s * 0.829 = 9.95 m/s (rounded)
- Vertical component: We are moving south, so the y-component is negative.
vertical component = magnitude of velocity * sin(angle)
vertical component = 12 m/s * sin(34°)
vertical component ≈ 12 m/s * 0.559 = 6.71 m/s (rounded)
Step 3: Summarize the components:
The velocity of 12 m/s at 34° south of west can be represented by the following components:
- Horizontal component: approximately -9.95 m/s
- Vertical component: approximately -6.71 m/s