# Projectile Motion: explaining why Vi=Vf

• shocklightnin
In summary, in projectile motion, the initial and final velocities can be shown to be equal by using the fact that the horizontal velocity does not change and the vertical velocity is affected by gravity. When the object reaches its maximum height and the vertical velocity is 0, it follows the same path back down resulting in the same velocity. This can be shown using a kinematic equation and by demonstrating that the time needed for the object to reach a certain height is equal to the time it takes for the object to fall from that height to the ground.
shocklightnin
How can i show that vi=vf in projectile motion using variables?

Could i just say that since its a parabola we know that vx isn't going to change, but that vy is because it is affected by gravity. so when it reaches max. height, and vy=0, you know that half of the flight is done, and that the object will follow the opposite path it took to get up there, to go back downwards resulting in the same velocity since gravity and vx is constant.

except i don't know how to show this using variables..

shocklightnin said:
How can i show that vi=vf in projectile motion using variables?

Could i just say that since its a parabola we know that vx isn't going to change, but that vy is because it is affected by gravity. so when it reaches max. height, and vy=0, you know that half of the flight is done, and that the object will follow the opposite path it took to get up there, to go back downwards resulting in the same velocity since gravity and vx is constant.

except i don't know how to show this using variables..

you may have to answer why Vx does not change... any forces?

And you could use one of your kinematic equations to show that in the vertical that Vyo is equal to - Vyf when in free fall and assuming the change in position in the vertical is equal to zero.

Welcome to PF!

Hi shocklightnin! Welcome to PF!
shocklightnin said:
How can i show that vi=vf in projectile motion using variables?

(I assume you mean for the initial and final heights being the same?)

One of the standard constant acceleration equations will do it.

You could show that the time needed for the mass to get up to height "h" is the same time it takes for the mass to get from height "h" to the ground. Then using this time calculate Vf, and it will = Vi.

## 1. What is projectile motion?

Projectile motion is the motion of an object that is thrown or launched into the air and moves along a curved path under the influence of gravity.

## 2. What is the initial velocity in projectile motion?

The initial velocity, denoted as Vi, is the velocity at which an object is launched or thrown into the air. It determines the speed and direction of the object's motion at the beginning of its trajectory.

## 3. Why is Vi equal to Vf in projectile motion?

In projectile motion, the acceleration due to gravity remains constant throughout the motion. This means that the final velocity, Vf, at any point in the trajectory is equal to the initial velocity, Vi. In other words, the speed and direction of the object do not change during its flight.

## 4. How does the angle of projection affect Vi=Vf in projectile motion?

The angle of projection determines the direction of the initial velocity, which in turn affects the trajectory of the object. However, the magnitude of the initial velocity remains the same regardless of the angle of projection, resulting in Vi being equal to Vf.

## 5. Can Vi be greater than Vf in projectile motion?

No, Vi cannot be greater than Vf in projectile motion. This is because the acceleration due to gravity always acts in the opposite direction of the initial velocity, causing the object to slow down. As a result, the final velocity will always be equal to or less than the initial velocity.

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