Balloon problem

CrossFit415

1. The problem statement, all variables and given/known data
Question: A hot-air balloon is ascending at the rate of 12m/s and is 80m above the ground when a package is dropped over the side.
a.)How long does the package take to reach the ground? b.)With what speed does it hit the ground?




2. Relevant equations
I know -- acceleration = -9.8 Initial velocity = 12 m/s and initial height = 80 m.

I know I have to use this formula
Xf = Vo + 1/2 (g) (T)²

Vo = 12 m/s
Xf = 80 m
g = -9.8 m/s²

I set Xf to 0.


How would I find Time?

Thanks

Doc Al

I think you mean:
Xf = Xo + Vo(T) - 1/2 (g) (T)²
where g = 9.8 m/s²
Time is the only unknown in the above quadratic equation, so solve for T.

CrossFit415

How would I go on about doing that? I cant seem to get T by itself in this equation.

NasuSama

That user is correct by the way because this is the form you should get. Well, since the object starts 80 m above the ground, x_0 = 80 obviously.

Here is the equation you get:

x_f = 80 + 12t - 4.9t²

It's not impossible to find t. To find t, use the quadratic equation as that user indicates. That is the way to find t. Remember that:

at² + bt + c = 0 OR c + bt + at² = 0

t = (-b ± √(b² - 4ac))/(2a)

OR

t = (-b + √(b² - 4ac))/(2a) or t = (-b - √(b² - 4ac))/(2a)

By letting the corresponding values be the a, b, c variables and then, solving for t, you should get the answer (it must be positive!).