SOLUTION: A gun fires a bullet almost straight up from the edge of a 100-foot cliff. If the bullet leaves the gun with a speed of 396 feet per second, its height at time t is given by h(t)=-

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Question 1054872: A gun fires a bullet almost straight up from the edge of a 100-foot cliff. If the bullet leaves the gun with a speed of 396 feet per second, its height at time t is given by h(t)=-16t2+396t+100, measured from the ground below the cliff.
When will the bullet land on the ground below the cliff? (Hint: What is its height when it lands? Remember that we are measuring from the ground below, not from the cliff.)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The bullet will hit the ground, which is
+100+ ft below the cliff ) when +h%28t%29+=+0+
-----------------------
+h%28t%29+=+-16t%5E2+%2B+396t+%2B+100+
+0+=+-16t%5E2+%2B+396t+%2B+100+
+-4t%5E2+%2B+99t+%2B+25+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-4+
+b+=+99+
+c+=+25+
+t+=+%28-99+%2B-+sqrt%28+99%5E2+-+4%2A%28-4%29%2A25+%29%29+%2F+%282%2A%28-4%29%29+
+t+=+%28-99+%2B-+sqrt%28+9801+%2B+400+%29%29+%2F+%28-8%29+
+t+=+%28-99+%2B-+sqrt%28+10201+%29%29+%2F+%28-8%29+
+t+=+%28-99+-+101%29+%2F+%28-8%29+
+t+=+%28+-200+%29+%2F+%28-8%29+
+t+=+25+
The bullet hits the ground in 25 sec
--------------------------------------
check:
+-4t%5E2+%2B+99t+%2B+25+=+0+
+-4%2A25%5E2+%2B+99%2A25+%2B+25+=+0+
+-2500+%2B+2475+%2B+25+=+0+
+-2500+%2B+2500+=+0+
+0+=+0+
OK
---------------------------------
Here's the plot. Note that it starts at +h%280%29+=+100+
as it should
+graph%28+500%2C+500%2C+-5%2C+30%2C+-300%2C+3000%2C+-16x%5E2+%2B+396x+%2B+100+%29+