# Why does this work? (X and Y independent)

• platina
In summary, the independence of the X and Y components of the ballistics cart allows it to shoot a projectile into the air and catch it when it lands.
platina
Why does this work?? (X and Y independent)

There is an image attached to refer to my question.

A ballistics cart traveling at constant velocity can shoot a projectile straight into the air and the projectile will be caught in the car when it lands because of the independence of the X and Y components.

In the image attached, because the cart is rolling down an incline it does not maintain a constant velocity. However, the ball is still caught. I don't understand why?

The projectile is maintaining the same horizontal velocity while it is in the air, but isn't the horizontal velocity of the cart - parallel to the ground, not parallel to the plane - increasing? After all, the cart is accelerating down the plane, so isn't it getting faster in the y-direction (perpendicular to the ground) and the x-direction (parallel to the ground)?

It just seems as though the projectile should fall behind the cart?

#### Attachments

• Plane Catch.jpg
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"A ballistics cart traveling at constant velocity" Why would it speed up?

In the image, the car is on an inclined plane, so it is accelerating down the plane.

Not necessarily, if there was a motor for instance, then there would be a constant velocity while going down a ramp

I agree with that, but the image I've attached is from a video clip that I have. There is no motor on the car; it is released from rest.

Even without a motor it can still travel down the ramp at a constant speed. The statement says it is moving at a constant velocity.

If there was no ramp and the car rolled on a horizontal surface at constant velocity, the ball would be caught, and I can clearly understand why. I'm confused with the scenario where the surface is not horizontal but angled with the horizontal as in the attached image.

The third statement in my original post says, "In the image attached, because the cart is rolling down an incline it does not maintain a constant velocity."

Since it is released from rest and it starts to roll down the incline, I'm assuming gravity causes it to accelerate down the plane, in which case it is gaining speed. So I assume it is accelerating down the ramp.

In the video clip I have the cart is clearly gaining speed as it moves down the ramp. Despite that fact, the ball is still caught.

Inclined Plane Reasoning

The model of the ballistic cart has to be clarified, so let’s model it as an object sliding down a frictionless incline.

My reasoning (not guaranteed valid) suggests that the ballistics cart will catch the ball regardless of the slope. Here is why:

Assume a Cartesian coordinate system in which the origin is on the incline at the point where the projectile is launched, the positive x-axis runs down the slope, and the positive y-axis is perpendicular to the slope in the “upward” direction. Since the projectile is launched perpendicular to the slope, its component of initial velocity in the x direction is the same as that of the cart.

The x component of the position of the cart and the projectile are always identical because they start out identical and are determined by the x component of acceleration due to gravity, which is the same for the cart and the projectile. When the projectile descends to the point where the y coordinate of the projectile equals the y coordinate of the cart, their positions will be the same.

Perhaps another reader will correct my faulty logic.

## 1. Why are X and Y considered independent variables?

Independent variables are considered as such because they are not affected by any other variables in the experiment. This means that changes in the independent variables will not be influenced by any other factors, allowing us to determine the true relationship between X and Y.

## 2. How do we know that X and Y have a cause-and-effect relationship?

We can determine a cause-and-effect relationship between X and Y by conducting a controlled experiment. This means that all other variables, except for X and Y, are kept constant. If changes in X consistently lead to changes in Y, then we can conclude that there is a causal relationship between the two variables.

## 3. What is the purpose of using X and Y as independent variables?

The purpose of using X and Y as independent variables is to understand the relationship between them. By manipulating X and observing the changes in Y, we can gain insight into how X affects Y and make predictions about the outcomes of future experiments.

## 4. Can we have more than two independent variables in an experiment?

Yes, we can have multiple independent variables in an experiment. However, this can make it more difficult to determine the exact relationship between all the variables and may require more complex statistical analysis.

## 5. How do we measure the impact of X on Y?

The impact of X on Y can be measured by calculating the correlation coefficient, which indicates the strength and direction of the relationship between the two variables. Other statistical measures, such as regression analysis, can also be used to measure the impact of X on Y.

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