SOLUTION: During a chemistry experiment, the cork in a 0.6-foot tall beaker with an effervescent so- lution pops off with an initial velocity of 23 feet per second. The quadratic model fo

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: During a chemistry experiment, the cork in a 0.6-foot tall beaker with an effervescent so- lution pops off with an initial velocity of 23 feet per second. The quadratic model fo      Log On


   



Question 399543: During a chemistry experiment, the cork in
a 0.6-foot tall beaker with an effervescent so-
lution pops off with an initial velocity of 23
feet per second. The quadratic model for the
situation is
h = −16t^2 + vt + s,
where v is the initial velocity, t is in seconds,
and s is the initial height.
How many seconds does it take for the cork
to hit the table?
Answer in units of sec.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Another way to ask the question is:
when is h equal to zero?
0+=+-16t%5E2+%2B+23t+%2B+.6
Multiply both sides by 10
-160t%5E2+%2B+230t+%2B+6+=+0
Divide both sides by 2
-80t%5E2+%2B+115t+%2B+3+=+0
Use the quadratic formula:
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+-80
b+=+115
c+=+3
t+=+%28-115+%2B-+sqrt%28+115%5E2+-+4%2A%28-80%29%2A3+%29%29%2F%282%2A%28-80%29%29+
t+=+%28-115+%2B-+sqrt%28+13225+%2B+960+%29%29%2F%28-160%29+
t+=+%28-115+%2B-+sqrt%28+14185+%29%29%2F%28-160%29+
t+=+%28-115+%2B+119.1008%29%2F%28-160%29+
t+=+%28+4.1008%29%2F%28-160%29+ (can't use a negative result)
also, the other root:
t+=+%28-115+-+119.1008%29%2F%28-160%29+
t+=+1.463 sec
check answer:
I'll see if this gives me h+=+0
-80t%5E2+%2B+115t+%2B+3+=+0
-80%2A1.463%5E2+%2B+115%2A1.463+%2B+3+=+0
-80%2A2.1404+%2B+168.245+%2B+3+=+0
-171.232+%2B+171.245+=+0
.013+=+0
This is too big an error, but I don't know what
happened. The method should be good, though