# Velocity vector along a parabola

• matatat
In summary, The behavior of a projectile thrown upwards in a gravitational field can be explained by Newton's second law. The velocity along the x-axis remains constant while the velocity along the y-axis remains linear due to the gravitational force only acting in the -y direction. This results in the velocity vector having the same initial and final velocity. To prove this, you can use kinematics and Newton's second law.
matatat
Hello, I'm new here and wasn't sure if this should be put into the homework section. It's not a homework question but the nature of the problem is homework-ish in nature I suppose.

Anyway I'm trying to understand why a velocity vector along a parabola would have the same initial velocity as its final velocity. I realize that velocity along the x-axis is a constant and I think the velocity along the y-axis remains linear. Although I can't figure out why both are so. Could someone explain this to me or direct me to where I would find the answer?

thanks
matt

Sorry also I forgot to mention that it makes sense in the fact that it will have enough velocity to reach a point y and its velocity will be zero and as it returns its velocity will return back to the original but negative. I was more so wondering how I could prove this with kinematics.

I assume you're talking about a projectile thrown upwards in a gravitational field, right?

Then the behavior you describe is derived directly from Newton's second law. Namely, the gravitational force only acts in the -y direction. Can you see why this leads to the velocity relationships?

## 1. What is a velocity vector along a parabola?

A velocity vector along a parabola is a vector that represents the direction and magnitude of an object's velocity as it moves along a parabola-shaped path. It is a combination of both the object's speed and its direction of motion.

## 2. How is the velocity vector calculated along a parabola?

The velocity vector along a parabola can be calculated using the derivative of the position vector with respect to time. This derivative gives the instantaneous velocity at any given point on the parabola.

## 3. What factors affect the velocity vector along a parabola?

The velocity vector along a parabola can be affected by factors such as the object's initial velocity, the force acting on the object, and any external forces such as friction or air resistance.

## 4. How does the velocity vector change along a parabola?

The velocity vector along a parabola changes as the object's speed and direction of motion changes. At the highest point of the parabola, the velocity vector will have a magnitude of 0 since the object is momentarily at rest. As the object moves towards the bottom of the parabola, the velocity vector will increase in magnitude until it reaches its maximum at the bottom of the parabola.

## 5. Can the velocity vector along a parabola be negative?

Yes, the velocity vector along a parabola can be negative. This indicates that the object is moving in the opposite direction of the positive direction chosen for the parabola. For example, if the positive direction is upwards, a negative velocity vector would indicate that the object is moving downwards along the parabola.

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