h(t) = -9.8t2 – 10t + 330, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground?

Asked on by shutto52

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beckden's profile pic

beckden | High School Teacher | (Level 1) Educator

Posted on

You want to solve

-9.8t^2 - 10t + 330 = 0

Use the quadradic formula

`t = (-b+-sqrt(b^2-4ac))/(2a)`

`t=(-(10)+-sqrt((10)^2-4(-9.8)(330)))/(2(-9.8))=(-10+-114. 175)/(-19.6)`

t = 6.335 sec  or -5.315 sec.

Obviously time is only positive so the answer is 6.335 seconds

shaznl1's profile pic

shaznl1 | High School Teacher | (Level 1) Salutatorian

Posted on

well the stone hits the ground when the height = 0

And here you have given a height function

so we only need to set it equal to zero.

Using quadratic formula ((-b+/-sqrt(b^2-4ac))/2a

plugging in all the numbers

a= -9.8 b- -10 c= 330

the answer is 6.335 or -5.315 and the unit is seconds.

Since time really couldn't be negative, (time machine?)

 the only legitmate answer to this question is 6.335 seconds

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