# Basic Motion Problem (Dropping Objects)

## Homework Statement

You are given a length of rope, tape and five rocks. The rocks must be attached in such a manner that when the rope is released, the sound of each rock hitting the ground is evenly spaced.

There must be a rock at the very bottom and the very top of the rope. When the rope is released, the bottom rock will be just above the ground. A stopwatch cannot be used (time cannot be recorded).

## Homework Equations

Any of the following kinematics equations:

d=1/2(Vf+Vi)t
Vf=Vi+at
d=Vit+1/2at^2
d=Vft-1/2at^2

## The Attempt at a Solution

a.) I understand that the rope will accelerate downwards due to gravity. This means that the rock at the top of the rope will have a faster final velocity just before impact than the rock at the bottom of the rope.
b.) Assuming that the bottom rock takes 0.1s to hit the ground I made the following calculations:

(Trying to space the sounds 0.2 second apart):

2nd rock from the bottom:

d = Vit+1/2at^2
d = (0)t + 1/2(9.81m/s^2)(0.3s)^2
d = 0.44 m

This means the second rock will be placed 0.44 m from the first rock (0.44 m from the bottom of the rope).

3rd rock from the bottom:

d = Vit+1/2at^2
d = (0)t + 1/2(9.81m/s^2)(0.5s)^2
d = 1.23 m

This means that the third rock will be placed 1.23 m from the bottom of the rope.

Is this the correct approach?

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