Initial vs final for a projectile

[judas_priest]

Homework Statement

A projectile is fired through the air. It is launched from the ground, and travels without interference from wind or air resistance, landing on a raised platform above the field.

Initial speed vs. final speed:

Initial vertical velocity vs. final vertical velocity

Initial horizontal velocity vs. final horizontal velocity:

Initial acceleration vs. final acceleration:

The attempt at a solution

For initial speed vs final speed, going by the basic definition, that is distance by time, they always stay in a ratio, so it doesn't change

For Initial vertical velocity vs. final vertical velocity, going by the basic definition again, that is displacement by time, till the highest point there's maximum displacement, therefore the ratio of displacement by time is the highest there. Even higher than just before landing, because it comes down, and hence the displacement decreases, also decreasing the ratio of d/t

Initial horizontal velocity vs. final horizontal velocity, there's no change because there's no air resistance or wind or any disturbance.

Initial horizontal velocity vs. final horizontal velocity. They're both the same in magnitude, just signs differ.

Please tell me where I'm wrong and why.

 

[PeterO]

Homework Statement

A projectile is fired through the air. It is launched from the ground, and travels without interference from wind or air resistance, landing on a raised platform above the field.

Initial speed vs. final speed:

Initial vertical velocity vs. final vertical velocity

Initial horizontal velocity vs. final horizontal velocity:

Initial acceleration vs. final acceleration:

The attempt at a solution

For initial speed vs final speed, going by the basic definition, that is distance by time, they always stay in a ratio, so it doesn't change

For Initial vertical velocity vs. final vertical velocity, going by the basic definition again, that is displacement by time, till the highest point there's maximum displacement, therefore the ratio of displacement by time is the highest there. Even higher than just before landing, because it comes down, and hence the displacement decreases, also decreasing the ratio of d/t

Initial horizontal velocity vs. final horizontal velocity, there's no change because there's no air resistance or wind or any disturbance.

Initial horizontal velocity vs. final horizontal velocity. They're both the same in magnitude, just signs differ.

Please tell me where I'm wrong and why.

In order:
Distance over time won't help - you should be able to work it out by understanding projectile motion..

Displacement over time won't help - you should be able to work it out by understanding projectile motion

Correct - you understand that side of projectile motion

Puzzling: you have addressed Horizontal velocity a second time rather than considering acceleration.

 

[judas_priest]

In order:
Distance over time won't help - you should be able to work it out by understanding projectile motion..

Displacement over time won't help - you should be able to work it out by understanding projectile motion

Correct - you understand that side of projectile motion

Puzzling: you have addressed Horizontal velocity a second time rather than considering acceleration.

Oops!
I meant "They're both the same in magnitude, just signs differ." for comparision of accelerations.

Anyways, how do I determine using projectile motion. No idea has struck me yet. If you could give me a start to my thinking.

 

[PeterO]

Oops!
I meant "They're both the same in magnitude, just signs differ." for comparision of accelerations.

Anyways, how do I determine using projectile motion. No idea has struck me yet. If you could give me a start to my thinking.

Not quite for acceleration: What is causing the acceleration?


The Vertical velocity in projectile motion is the same as for an object thrown straight up.

If it comes back to original height, it slows down on the way up, then speeds up on the way back down - regaining all the speed it lost - arriving back at the same speed that it began (but different velocity because of the direction.

If it gets "interupted" on the way down, and doesn't come back to the original level, then it does not completely regain its original speed.

How was that for a hint?

 

[Nickie]

Your response is mostly correct. The main thing I would add is that the final vertical velocity will be the same as the initial vertical velocity, but with a negative sign since the projectile is now moving in the opposite direction (downward) compared to its initial direction (upward). This is due to the acceleration of gravity, which causes the projectile to accelerate downward as it reaches its highest point and then continues to accelerate as it falls towards the ground.

Additionally, it is important to note that while the horizontal velocity does not change, the horizontal displacement will continue to increase until the projectile reaches its landing point on the raised platform. This is because the projectile will continue to move horizontally at a constant speed while also being pulled downward by gravity.

For the initial and final acceleration, it is important to clarify that the initial acceleration is due to the force of the launch, while the final acceleration is due to the force of gravity. The initial acceleration will be greater as it is solely determined by the force of the launch, while the final acceleration will decrease as the projectile reaches its highest point and then increases again as it falls towards the ground.

Overall, your understanding of the initial and final values for a projectile is correct, but it is important to clarify the role of gravity and the fact that the horizontal displacement will continue to increase even though the horizontal velocity remains constant.