SOLUTION: Hello, I need help with this problem: The height, in feet, of a rocket t seconds after blast-off is given by a formula h=1260t-16t^2. After how many seconds will the roc

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Hello, I need help with this problem: The height, in feet, of a rocket t seconds after blast-off is given by a formula h=1260t-16t^2. After how many seconds will the roc      Log On


   

Question 104568: Hello,

I need help with this problem:

The height, in feet, of a rocket t seconds after blast-off is given by a formula h=1260t-16t^2. After how many seconds will the rocket first reach a height of 23,400 feet?

Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
h=1260t-16t%5E2
1260t-16t%5E2=23400
-16t%5E2%2B1260t-23400=0
Use the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where
a=-16, b=1260, and c=-23400

t+=+%28-1260+%2B-+sqrt%28+1587600-1497600%29%29%2F%28-32%29%29+
t+=+%28-1260+%2B-+sqrt%28+90000%29%29%2F%28-32%29%29+
t+=+%28-1260+%2B-+300%29%2F%28-32%29%29+
t+=+%28-1560%29%2F%28-32%29%29+ and
t+=+%28-960%29%2F%28-32%29%29+
t=48.75 seconds
t=30 seconds
Since your looking for the first time, pick the earliest time.
t=30 seconds.
Why two answers? First when the rocket is going up and then when the rocket's coming down, as shown in the graph below, with the horizontal axis equal to h=23,400 feet.
+graph%28+300%2C+300%2C+28%2C+50%2C+-5000%2C5000%2C+-16x%5E2%2B1260x-23400%29+