How High Was the Building From Which the Water Balloon Was Dropped?

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SUMMARY

The height of the building from which the water balloon was dropped is calculated to be 48.3 meters. The calculation uses the principle of conservation of energy, equating potential energy (PE) to kinetic energy (KE). The formula applied is h = v² / (2g), where v is the velocity of the balloon at impact (30.3 m/s) and g is the acceleration due to gravity (9.81 m/s²). The final height includes the height of the person (1.5 meters) plus the calculated height of the building (46.8 meters).

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A prankster drops a water balloon from the top of a building on an unsuspecting person on the sidewalk below. If the balloon is traveling at 30.3m/s when it strikes a person's head ( 1.5m above ground). How tall is the building? Neglect air resistance.

PE= KE
mgh=.5*mv^2
h= v^2/2g
h=(30.3m/s)^2/(2*9.81m/s/s)
h=918.09 m^2/s^2 / 19.62 m/s/s
h= 46.8m

total height = 1.5m + 46.8m = 48.3m
is this right? Is the sig figs right?

Thank you
 
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Looks right.
 
easy.
 

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