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