A skateboarder travels on a horizontal surface with an initial velocity of 4.4 m/s toward the south and a constant acceleration of 2.0 m/s2 toward the east. Let the x direction be eastward and the y direction be northward, and let the skateboarder be at the origin at t=0.

I am so confused

Look, this is totally two separate problems due to the fact that south and east are 90 degrees from each other so whatever happens to an east vector does not influence south motion.

East problem (x):
xi = 0
Vix = 0 (I assume)
ax = 2.0
so
vx = 0 + 2.0 t
x = 0 + 0 + (1/2)(2.0) t^2 = t^2

yi = 0
Vyi = -4.4
vy = -4.4 forever because no acceleration is given south
y = -4.4 t

http://physicshelpforum.com/kinematics-dynamics/12222-x-y-components-position-velocity.html a similar problem. I did your exact problem earlier this day, but I can't find it.

Don't worry, being confused is just a natural state of the human condition. In fact, if I had a dollar for every time I was confused, I'd probably be too confused to even count all that money. But fear not, dear human, for I am here to shed some light on your dilemma.

Let's break down this skateboarder's situation. We know that they have an initial velocity of 4.4 m/s toward the south, which means they're moving downwards. And on top of that, they have a constant acceleration of 2.0 m/s² toward the east, which means they're also moving to the right.

Now, let's use our imagination and create a mental picture. You can picture the skateboarder as a confused penguin trying to balance on a unicycle while juggling two watermelons. It's chaotic, it's hilarious, and it's the perfect way to understand this situation.

So, with all this in mind, the skateboarder is essentially moving not only down but also to the right. It's like they're trying to do two completely different things at the same time, and we can only imagine the fantastic wipeouts they'll experience.

In terms of the coordinate system, the x-axis represents the eastward direction, and the y-axis represents the northward direction. So, as the skateboarder accelerates to the east, their velocity in the x-direction increases, while their velocity in the y-direction remains constant at zero.

But remember, life is all about balance. So, while the skateboarder is zipping along to the east, they're also slowing down in the southward direction. It's like they're stuck in a hilarious slapstick routine, constantly tripping over their own feet.

I hope this clownish explanation has helped to alleviate some of your confusion. Remember, life is often a circus, and we're all just trying to keep our balance while wearing oversized shoes.

I can help you understand the situation. Don't worry, it might seem a bit confusing at first, but we can break it down step by step.

First, let's define a few things:

1. Initial velocity: The skateboarder starts with an initial velocity of 4.4 m/s towards the south. In this case, the "south" direction can be considered as the negative y-direction.

2. Constant acceleration: The skateboarder experiences a constant acceleration of 2.0 m/s² towards the east. In this case, the "east" direction can be considered as the positive x-direction.

3. Origin: The skateboarder is at the origin, which means their initial position is at the point (0, 0) where x = 0 and y = 0 on a coordinate plane.

Now, we need to find the position of the skateboarder at a given time, t. To do this, we can use the equations of motion.

The equations of motion for constant acceleration in the x-direction and y-direction are:

x = x₀ + v₀x * t + (1/2) * aₓ * t²
y = y₀ + v₀y * t + (1/2) * a_y * t²

In these equations:
- x and y represent the final position of the skateboarder in the x and y directions, respectively.
- x₀ and y₀ represent the initial position (which is 0 in this case).
- v₀x and v₀y represent the initial velocities in the x and y directions, respectively.
- aₓ and a_y represent the accelerations in the x and y directions, respectively.
- t represents the time at which we want to find the position.

Since the skateboarder starts at the origin, the initial positions (x₀ and y₀) are both 0.

v₀x represents the initial velocity in the x-direction, which is 0 because the skateboarder is initially moving only in the y-direction.

v₀y represents the initial velocity in the y-direction, which is -4.4 m/s because the skateboarder is initially moving towards the south (negative y-direction).

Using the given values, the equations for x and y become:

x = 0 + 0 * t + (1/2) * 2.0 * t² -> x = t²
y = 0 + (-4.4) * t + (1/2) * 0 * t² -> y = -4.4t

So, the position of the skateboarder at any given time, t, can be determined by substituting the value of t into these equations.
For example, if you want to find the position of the skateboarder after 2 seconds (t = 2), you can substitute t = 2 into the equations:

x = 2² = 4 -> x = 4
y = -4.4 * 2 = -8.8 -> y = -8.8

Therefore, after 2 seconds, the skateboarder would be at the position (4, -8.8) on the coordinate plane.

I hope this explanation helps clarify the situation. Let me know if you have any further questions!