A weather balloon is released and rises vertically such that its distance s(t) above the ground during the first 10 seconds of flight is given by s(t) = 6 + 2t + t^2, where s(t) is in feet and t is in second. Find the velocity of the balloon at the instant the balloon is 50 ft above the ground.

Question

A weather balloon is released and rises vertically such that its distance s(t) above the ground during the first 10 seconds of flight is given by s(t) = 6 + 2t + t^2, where s(t) is in feet and t is in second.  Find the velocity of the balloon at the instant the balloon is 50 ft above the ground.

anonymous · Answer

v(t)=ds(t)/dt=2+2t
s(t)=50 when t^2+2t+6=50
solve for t, and substitute in v(t)

anonymous · Answer

Yea, I had the first part but I couldn't get the correct answer when finding the solution as I'd get -2 +- sqrt(176) / 2

anonymous · Answer

Ok,
I get x=-1+- 3sqrt(5)

anonymous · Answer

Lemme try it on a new sheet of paper...
Thanks for being so helpful.

anonymous · Answer

I got it!  I think...I'm getting 180 under the square root now...so I think it will come out right.

anonymous · Answer

$$t=-1+3\sqrt{5}$$
is positive
from which
$$v(t)=2-2+6\sqrt{5} = 6\sqrt{5}$$

anonymous · Answer

I'm kinda lost now.  Where are you getting 2-2+6sqrt5 from?  The derivative for s(t) is 2t + 2

anonymous · Answer

I received the same answer as you for the value of t, though.

anonymous · Answer

ok ,then 2+2t = 2+2(-1+3sqrt(5))= 2-2+2*3*sqrt(5) = 6sqrt(5)

anonymous · Answer

where the hell am i messing up?  im getting 2sqrt5 instead of 3sqrt5 somehow...that's wrong.

anonymous · Answer

The equation is x^2+2x-44=0, right?

anonymous · Answer

Never mind, ignore me...I'm an idiot.  I see how you got the answer.  Thanks!

anonymous · Answer

Never call yourself an idiot. Someone might believe you... ;-)

anonymous · Answer

I'm making things too complex on myself by jumping over steps such as simplifying and stuff...in turn it's causing me to work too hard at getting to the answer and it doesn't APPEAR right even though it is once broken down.  Idiot is as idiot does and what I did would be classified as idiotic.  :P  Good answer given...enjoy your afternoon!