SOLUTION: During a baseball game, a player’s ball hit into the outfield is modeled by the equation h = –16t2 + 65t. A bird flying across the field follows the path modeled by the equation h

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: During a baseball game, a player’s ball hit into the outfield is modeled by the equation h = –16t2 + 65t. A bird flying across the field follows the path modeled by the equation h       Log On


   

Question 822621: During a baseball game, a player’s ball hit into the outfield is modeled by the equation h = –16t2 + 65t. A bird flying across the field follows the path modeled by the equation h = 8t + 20. Let t be the time since the ball is hit and h be the height. What do the intersection points of the equations represent?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Ball's equation:
(1) +h%28t%29+=+-16%2At%5E2+%2B+65t+
Bird's equation:
(2) +h%28t%29+=+8t+%2B+20+
-------------------
To find the intersections, I'll say
that +h%28t%29+ is the same for both
+-16%2At%5E2+%2B+65t++=+8t+%2B+20+
+-16t%5E2+%2B+57t+-+20+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-16+
+b+=+57+
+c+=+-20+
+t+=+%28-57+%2B-+sqrt%28+57%5E2+-+4%2A%28-16%29%2A%28-20%29+%29%29+%2F+%282%2A%28-16%29%29+
+t+=+%28-57+%2B-+sqrt%28+3249+-+1280+%29%29+%2F+%28-32%29+
+t+=+%28-57+%2B-+sqrt%28+1969+%29%29+%2F+%28-32%29+
+t+=+%28-57+%2B+44.373%29+%2F+%28-32%29+
+t+=+%28+-12.627+%29%2F%28-32%29+
+t+=+.395+
and, also:
+t+=+%28-57+-+44.373%29+%2F+%28-32%29+
+t+=+%28+-101.373+%29%2F%28-32%29+
+t+=+3.168+
--------------
These are the times at which the heights of the
bird and the ball are the same
Here's the plot of both trajectories:
+graph%28+400%2C+400%2C+-2%2C+6%2C+-10%2C+80%2C+-16x%5E2+%2B+65x%2C+8x+%2B+20+%29+
---------------
What I would say the intersections represent is that
if the bird is 20 feet directly above the batter at the
exact moment the ball is hit, the 1st intersection is
the height and time of the collision.
-------------
If the bird wasn't exactly overhead, but followed the same
path, the 2nd intersection is the only height and time
for a possible collision.