# Relative Impact Speed

1. Feb 14, 2007

### 2Silent

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

One dimensional equations

3. 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.