Velocity, time, acceleration etc

[lauriecherie]

Homework Statement

A hot air balloon is ascending at the rate of 13 m/s and is 93 m above the ground when a package is dropped over the side. How long does the package take to reach the ground? With what speed does it hit the ground?

Homework Equations

x(t)= initial position + final velocity * time

v(t)= (acceleration * time) + initial velocity

x(t)= .5 * (acceleration * (time^2)) + (initial velocity * time) + inital position

x= initial position * (average velocity * time)

average velocity= (final velocity - initial velocity) / (2)

(final velocity^2) - (initial velocity^2) = 2 * acceleration * change in position

The Attempt at a Solution

I manipulated equation 4 to solve for time and got 7.15 s, which is wrong. Then I began thinking "Do I need to double this time?" Is it supposed to be 14.31 s?
For question 2, I used the last equation to solve for final velocity and got 50.86 m/s which it also marked incorrectly. Can anyone please explain this to me? I seem to be having trouble with motion in two direction thing...

 

[LowlyPion]

It's only motion in one dimension. You just need to set up your equation.

Use:

x = Xo + Vo*t - 1/2*g*t²

Xo is your initial height. Vo is your velocity (+ is up)

The third term is -, as g is down.

 

[lauriecherie]

It's only motion in one dimension. You just need to set up your equation.

Use:

x = Xo + Vo*t - 1/2*g*t²

Xo is your initial height. Vo is your velocity (+ is up)

The third term is -, as g is down.

I'm solving for time. I don't know how to manipulate that equation to get time by itself. Is there another one on here I can use?

 

[LowlyPion]

When you plug in the values you are left with a quadratic equation.

Use the quadratic formula to solve using the coefficients of the terms.

http://en.wikipedia.org/wiki/Quadratic_equation#Quadratic_formula