How do you determine the height for Part B of this question?

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1 Answer
Jul 7, 2016

Answer:

#14#
#47.68ms^-1#, rounded to two decimal places.
#142J#

Explanation:

Let height of the building be #=h " "m#
After the wrench is dropped from the roof top, the kinematic equation is given by
#v^2-u^2=2gs# ......(1)
where #v, u and g# are final velocity after dropping distance #s#, initial velocity and acceleration due to gravity respectively. Let #g=9.8ms^-2#

Let us find out the distance dropped when workman standing at the eighth floor observes the wrench. (for simplicity eyes of worker assumed at the floor level)
#(33.1)^2-0^2=2xx9.8xxs#
#=>s=(33.1)^2/(2xx9.8)#
#=>sapprox55.9 m#
Since the floors above the first are of height #8m# each
Hence number of floors above the eighth floor#=55.9/8#
#=7#, rounded to nearest digit as number of floors can not be a fraction.
Total number of floors of the building #=7+7=14#
We need to remember that the workman standing on the eighth floor has only seven floors below him.

Height of the building #h=12.0+13xx8.00=116.00m#
(First floor is of #12.0 m# and all other floors are of #8.00 m # height)
From (1) velocity #v# when the wrench hits the ground
#v^2=2xx9.8xx118.00#
#v=47.68ms^-1#, rounded to two decimal places.

Kinetic energy of wrench when it hits the ground#=mgh#
#=0.125xx9.8xx116=142J#

(All its potential energy while at the roof gets converted into its kinetic energy as it hits the ground.
It can also be calculated using the expression #KE=1/2mv^2#)