Course Contents .. Assignment 1-Units and 1D Motion 2.56-Falling Objects 2.56-Fa

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Course Contents .. Assignment 1-Units and 1D Motion 2.56-Falling Objects 2.56-Falling Objects Part A Suppose you drop a rock from rest into a dark well and, using precision equipment, you measure the time for the sound of a splash to return, Negiecting the time required for sound to travel up the wel, calculate the distance to the water if the sound returns in 2.2500 24.8 m You are correct. Your receipt no. is 161-6897 Part B Now calculate the distance taking into account the time for sound to travel up the well. The speed of sound is 340.00 m/s in this well Tries 2/10 Preyious Tres © 1998-2017 by Florida State Universty, Ali nghts reserved s parts and in any form, including pasting on the web or in printed version, a for use by the students enroiled in this counse only Any distribution of the contents in whole or in violation ofthe copyright laws and the FSU honor codes. This discussion is closed. 3 4

Explanation / Answer

A. given, time taken for the stone to splash on the water, t = 2.25 s ( disregarding thetime taken by sound to come back)

initial velocity of stone, u = 0

so using h = ut + 0.5gt^2

h = depth of well = 0.5*9.81*2.25^2 = 24.831 m

B> Now considering time taken by sound to come back

time taken by sound to come back = t' = h/v [ where v is speed of sound]

time taken by stone to splash on the well, t" = 2.25 - t' = 2.25 - h/v [ v = 340 m/s]

so h = 0.5*g(t")^2

2h = g*(2.25 - h/v)^2 = g(5.0625 + h^2/v^2 - 4.5h/v)

2v^2*h/g = 5.0625*v^2 + h^2 - 4.5hv

h^2 -25097.788h + 585225 = 0

SOLVING FOR H

WE GET

h = 23.339 m

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