If a stone is tossed from the top of a 270 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 270, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground?

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If a stone is tossed from the top of a 270 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 270, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground?

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Answer 1 · 2015-06-28T15:36:14

Solve $h(t) = 0$ using the quadratic formula to get:

$t = (10+-sqrt(10^2-(4xx-9.8xx270)))/(2xx-9.8)$

$t~=4.76$ or $t~=-5.78$

Discard the negative solution to get $t ~= 4.76$ seconds.

Explanation:

$h(t)$ is of the form $at^2+bt+c$ , with $a=-9.8$ , $b=10$ and $c=270$

The roots of $h(t) = 0$ are given by the formula:

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

$= (10+-sqrt(10^2-(4xx-9.8xx270)))/(2xx-9.8)$

$=-(10+-sqrt(10684))/19.6$

$~=-(10+-103.36)/19.6$

$t~=4.76$ or $t~=-5.78$

Discard the negative solution to get $t ~= 4.76$ seconds.

The negative solution relates to a prequel to the story in which the stone is thrown up from the ground $5.78$ seconds before it passes the top of the building on the way back down.

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If a stone is tossed from the top of a 270 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 270, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground?

1 Answer

Explanation:

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