SOLUTION: A rocket is launched into the air. The height in feet, of the rocket, above the ground is given by h(t)=-4.9t(squared) + 192t, where t represents the time in seconds after the lau

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A rocket is launched into the air. The height in feet, of the rocket, above the ground is given by h(t)=-4.9t(squared) + 192t, where t represents the time in seconds after the lau      Log On


   

Question 122161: A rocket is launched into the air. The height in feet, of the rocket, above the ground is given by h(t)=-4.9t(squared) + 192t, where t represents the time in seconds after the launch. (Hint:draw a picture)
#1. How long is the rocket in the air before it reaches the ground?
#2. How long does it take the rocket to reach its highest point?
#3. How high is the rocket at its highest point? I know that to find this answer I use the formula for the line of symmetry, and the vertex is the highest point..I think that it is 19.6 feet if I did it right.
The other questions I do not know how to do.
Thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I can plot this
+graph%28+600%2C+600%2C+-5%2C+50%2C+-50%2C+2000%2C+%28-4.9%29%2Ax%5E2+%2B+192x%29+
h%28t%29+=+-4.9t%5E2+%2B+192t
-------------------------------
(1) I need to find the change in t when th3e
rocket goes from (t,h) = (0,0) to (t,0) where t is the
time to fall back to earth
h%28t%29+=+-4.9t%5E2+%2B+192t
0+=+-4.9t%5E2+%2B+192t
t%2A%28-4.9%2At+%2B+192%29+=+0
One solution is t+=+0 This is the point (0,0)
The other solution is -4.9%2At+%2B+192+=+0
4.9%2At+=+192
t+=+39.184 sec (this agrees closely with graph)
-------------------------------------------------
(2) The highest point is where t+=+%28-b%29%2F%282a%29 when
equation is in the form +ax%5E2+%2B+bx+%2B+c+=+0
a+=+-4.9
b+=+192
t+=+%28-192%29+%2F+%28-9.8%29
t+=+19.592 sec (this is exactly 1/2 the time to hit the ground)
---------------------------------------------------
(3) I need to find h%5Bt%5D when t+=+19.592
h%5Bmax%5D+=+-4.9t%5E2+%2B+192t
h%5Bmax%5D+=+-4.9%2A%2819.592%29%5E2+%2B+192%2A%2819.592%29
h%5Bmax%5D+=+-1880.848+%2B+3761.664
h%5Bmax%5D+=+1880.816 ft (this agrees with graph, also)