SOLUTION: Gabe drops a hammer from an apartment that is 30 meters above the ground. The height of the hammer in meters, ℎ, after t seconds is modeled by the function shown. ℎ(

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Question 1057399: Gabe drops a hammer from an apartment that is 30 meters above the
ground. The height of the hammer in meters, ℎ, after t seconds is modeled by
the function shown.
ℎ(t) = −t^2 − 2t + 30
Find the approximate number of seconds it will take for the hammer to hit the
ground. Round your answer to the nearest whole number.
□ 0
□ 5
□ 10
□ 30
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The hammer has to fall 30 m
and the height, +h%28t%29+=+0+
+-t%5E2+-+2t+%2B+30+=+0+
use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-1+
+b+=+-2+
+c+=+30+

+t+=+%28+2+%2B-+sqrt%28+4+%2B+120+%29%29+%2F+%28-2%29+
+t+=+%28+2+%2B-sqrt%28+124+%29+%29+%2F+%28-2%29+
+t+=+%28+2+-+11.136+%29+%2F+%28-2%29+ ( I used the negative square root to make
the time, +t+, come out positive )
+t+=+%28+-9.136+%29+%2F+%28-2%29+
+t+=+4.568+
The hammer hits the ground in 5 sec
( rounded off )
--------------------------------------
check:
+-t%5E2+-+2t+%2B+30+=+0+
+-1%2A%284.568%5E2%29+-+2%2A4.568+%2B+30+=+0+
+-1%2A20.867+-+9.136+%2B+30+=+0+
+-30.003+%2B+30+=+0+
OK -close enough