SOLUTION: Please help me solve this word problem: A disc is thrown into the air and follows a path modeled by the function h(t)=7.8+22t-5t^2, where time, t, is in seconds and height h(t) is

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me solve this word problem: A disc is thrown into the air and follows a path modeled by the function h(t)=7.8+22t-5t^2, where time, t, is in seconds and height h(t) is       Log On


   

Question 882146: Please help me solve this word problem: A disc is thrown into the air and follows a path modeled by the function h(t)=7.8+22t-5t^2, where time, t, is in seconds and height h(t) is in meters. Determine when the ball will land to the nearest hundredth.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The equation is a parabola
+h%28t%29+=+-5t%5E2+%2B+22t+%2B+7.8+
The ball is released at +t+=+0+
and +h+=+7.8+
-----------------------------
You want to know what +t+ is
when +h+=+0+ for the 2nd time
( the ball comes back to earth )
---------------------------
This is the same as finding both of
the roots of the equation
Set +h%28t%29+=+0+ and use the
quadratic formula to find roots
----------------------------
+-5t%5E2+%2B+22t+%2B+7.8+=+0+
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-5+
+b+=+22+
+c+=+7.8+
+t+=+%28+-22+%2B-+sqrt%28+22%5E2+-+4%2A%28-5%29%2A7.8+%29%29+%2F+%282%2A%28-5%29%29+
+t+=+%28+-22+%2B-+sqrt%28+484+%2B+156+%29%29+%2F+%28-10%29+
+t+=+%28+-22+%2B-+sqrt%28+640+%29%29+%2F+%28-10%29+
+t+=+%28+-22+-+8%2Asqrt%2810%29+%29+%2F+%28-10%29+
+t+=+2.2+%2B+.8%2Asqrt%2810%29+
+t+=+2.2+%2B+.8%2A3.1623+
+t+=+2.2+%2B+2.53+
+t+=+4.73+
The ball lands in 4.73 sec
Note that I chose the largest positive root as the
correct one for when the ball will land
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+6%2C+-5%2C+35%2C+-5x%5E2+%2B+22x+%2B+7.8+%29+
+t+ at +h+=+0+ looks pretty close to +4.73+