- #1

UMich1344

- 27

- 0

## Homework Statement

A ball is dropped from rest from the top of a building and strikes the ground with a speed

*v*

_{f}. From ground level, a second ball is thrown straight upward at the same instant that the first ball is dropped. The initial speed of the second ball is

*v*

_{0}=

*v*

_{f}, the same speed with which the first ball will eventually strike the ground. Ignoring air resistance, decide whether the balls cross paths at half the height of the building, above the halfway point, or below the halfway point. Give your reasoning.

## Homework Equations

Kinematics equations.

## The Attempt at a Solution

Strictly conceptually, we know that when something is thrown up, its initial velocity is greater than its final velocity (at its peak). When something is dropped, its initial velocity is less than its final velocity (at the ground).

We can conclude that when an object travels with a greater velocity over a certain amount of time than a second object does, the larger the displacement of the first object will be.

When something is dropped, it speeds up as its displacement becomes larger. On the other hand, when something is thrown up, it slows down as its displacement becomes larger.

With this reasoning we can conclude that the balls will cross paths above the halfway point of the building because the ball that is thrown up will have a greater displacement than the ball that is dropped when they cross paths.

Is that correct?

I want to back up my answer with some math work too. However, I'm not sure how to go about it. I know I can refer to the height of the building as

*h*and then solve for the point at which the two balls cross and compare my answer to

*h*in order to see if the point is greater than 0.5

*h*. I just don't know exactly how to set it up.