SOLUTION: A circus acrobat is shot out of a cannon with an initial upward speed of 50 ft/s. If the acrobat leaves the cannon 4 ft above the ground, how long will it take him to reach a net

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A circus acrobat is shot out of a cannon with an initial upward speed of 50 ft/s. If the acrobat leaves the cannon 4 ft above the ground, how long will it take him to reach a net       Log On


   

Question 852983: A circus acrobat is shot out of a cannon with an initial upward speed of 50 ft/s. If the acrobat leaves the cannon 4 ft above the ground, how long will it take him to reach a net that is 10 ft above the ground?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The equation is:
+h%28t%29+=+-16t%5E2+%2B+50t+%2B+4+
where +t+ is in seconds and +h+ is in feet
Note that when +t+=+0+, +h%28t%29+=+4+
as it should
------------------
You need to find +t+ when +h%28t%29+=+10+
+10+=+-16t%5E2+%2B+50t+%2B+4+
+-16t%5E2+%2B+50t+-+6+=+0+)
+-8t%5E2+%2B+25t+-+3+=+0+
Use the quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-8+
+b+=+25+
+c+=+-3+
+t+=+%28-25+%2B-+sqrt%28+25%5E2+-+4%2A%28-8%29%2A%28-3%29+%29%29+%2F+%282%2A%28-8%29%29+
+t+=+%28-25+%2B-+sqrt%28+625+-+96+%29%29+%2F+%28-16+%29+
+t+=+%28-25+%2B-+sqrt%28+529+%29%29+%2F+%28-16+%29+
+t+=+%28-25+%2B-+23%29+%2F+%28-16+%29+
----------------------------
+t+=+-48+%2F+%28-16%29+
+t+=+3+ sec
This is the answer I want, the other answer is the time
immediately after the cannon is fired:
+t+=+-2%2F%28-16%29+
+t+=+1%2F8+
------------------------
The acrobat hits the net 3 sec after the cannon fires
Here's the plot:
+graph%28+500%2C+500%2C+-1%2C+5%2C+-5%2C+50%2C+10%2C+-16x%5E2+%2B+50x+%2B+4+%29+