The distance a body falls varies directly as the square of the time it falls. IF an object falls 64 feet in 2 seconds, how long will it take to fall 256 feet?

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Answer 1 · 2018-06-15T14:15:43

4 seconds

Distance varies directly as the square of the time it falls
#=> d=kt^2#

Initial condition #->#64 feet in 2 second #=>d=kt^2->64=k2^2#

#64=k2^2#

Divide both sides by #4larr (2^2=4)#

#64/4=k = 16#

Giving #d=16t^2#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Set #d=256# giving:

#256=16t^2#

Divide both sides by 16

#16=t^2#

Square root both sides

#t=4" seconds"#