The height h in feet of an object after t seconds is given by the fraction h = -16t^2 + 30t + 8. How long will it take the object to hit the ground? Round answer to the nearest thousandth?

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Answer 1 · 2017-06-06T06:30:53

It will take #2.112# seconds for object to hit ground.

The height of ground level is considered as #0#.

as #h=-16t^2+30t+8#, it will be zero, when

#-16t^2+30t+8=0#

or #16t^2-30t-8=0# anddividing by #2#

#8t^2-15t-4=0#

Using quadratic formula #t=(-(-15)+-sqrt((-15)^2-4xx8xx(-4)))/16#

= #(15+-sqrt(225+128))/16#

= #(15+-sqrt353)/16#

= #(15+-18.7883)/16#, but as we cannot have #t# negative

#t=33.7883/16=2.112# seconds