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
George C.
Jun 28, 2015

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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