Ignoring air resistance, which case will make it hit the ground with the greatest speed?

Throw the egg up.

Throw the egg down.

Both up and down will have the same result.

Drop the egg from rest.

More information is needed to answer.

Ignoring air resistance, dropping the egg from rest will make it hit the ground with the greatest speed.

if Vi is downward it will hit going faster

think what happens if Vi ----> infinity downward (upward is + )
gravity becomes unimportant compared to Vi t

You are correct. If the initial velocity (Vi) is infinitely downward, the effect of gravity becomes unimportant when compared to the enormous speed of the egg. In that case, the egg would hit the ground with a very high velocity.

To determine which case will make the egg hit the ground with the greatest speed, we need to consider the principles of motion and potential energy.

First, let's understand that when an object is thrown up or down, its initial velocity will affect its final velocity when it reaches the ground.

If we ignore air resistance, the only force acting on the egg will be gravity. When the egg is thrown up, it will experience a negative acceleration due to the Earth's gravitational pull, causing it to slow down and eventually reverse its direction. Then, as it falls back down, it will accelerate towards the ground due to gravity, increasing its speed.

Conversely, when the egg is thrown down, it will experience a positive acceleration due to gravity, causing it to accelerate even more towards the ground compared to a dropped egg.

So, based on this understanding, throwing the egg down will make it hit the ground with the greatest speed, as it benefits from an initial positive acceleration due to gravity.

Therefore, the correct answer is "Throw the egg down."