What Is the Best Action to Minimize Impact Speed in a Falling Physics Problem?

[2Silent]

Homework Statement

A curious Physics student is inspecting A tower. He slips from a platform near the top and begins to fall straight down. Directly beneath him is an empty elevator at rest part way up the tower wall, and there is a set of control buttons on the platform from which he is slipping. If he does nothing, he will strike the stationary elevator. If he hits the down button, the elevator instantly starts down at a constant speed and he will catch it at a lower point, but before it hits the ground. If he hits the up button, the elevator instantly starts up at the same constant speed and he will meet it at a higher point. Natuerally he wishes to minimize his relative impact speed. What should the Physics student do?

Homework Equations

One dimensional equations

The Attempt at a Solution

Xop = 0.0 m
a = +9.8 m/s
Vop = 0.0 m/s
tp = te
_ _ _ _ _ _

Vo = Ve
Xoe = +h
ae = 0.0 m/s
Ve = ve
te = tp

_ _ _ _ _ _

Xe = Xp

I know that the best method is to keep the elevator stationary but I'm finding it difficult to prove why. I know that going down and up have an equal and opposite relative impact speed.

 

[lippyka]

I think that the Physics student should not hit any buttons since the relative impact speed will be the same as if he had done nothing.

 

[m2003]

However, if the elevator is stationary, the student will not experience any relative impact speed at all. This is because the elevator and the student will have the same velocity and direction when they meet. Therefore, the impact speed will be zero.

To further support this, we can use the equation for relative velocity:

Vrel = Vp - Ve

If the elevator is stationary (Ve = 0), then the relative velocity is simply equal to the student's velocity (Vrel = Vp). This means that the student and the elevator will have the same velocity when they meet, resulting in a zero relative impact speed.

Additionally, if the student chooses to hit the down button, the elevator will start moving down at a constant speed, which means that the relative velocity will be constantly increasing until the elevator meets the student. This will result in a higher relative impact speed than if the elevator was stationary.

Similarly, if the student hits the up button, the elevator will start moving up at a constant speed, resulting in a decreasing relative velocity. However, the relative impact speed will still be higher than if the elevator was stationary.

In conclusion, the best option for the student is to do nothing and let the elevator remain stationary. This will minimize the relative impact speed and ensure the student's safety.