A sand bag is dropped out of a balloon traveling upward at speed of 2.3m/s. A kiddo drops a bag at the instant the balloon is 34m above the ground. How long does it take the sand bag to hit the ground? I got -2.41s why?

h = 0

Hi = 34
Vi = + 2.3
(1/2) a = -g/2 = -4.9

h = Hi + Vi t - 4.9 t^2

0 = 34 + 2.3 t - 4.9 t^2

4.9 t^2 - 2.3 t - 34 = 0

t = [ 2.3 +/- sqrt(5.29 + 881) ]/ 9.8

t = [ 2.3 +/- 29.8 ]/9.8

t = 3.27 OR -2.8
the negative t was when it would have been at ground on the way up if it were thrown up from ground and is not relevant.

I don't understand the negative. Would it be wrong if I put the negative answer if they're asking how long it takes the sand bag to hit the ground?

Yes, the negative is unreal and wrong.

The trajectory is a parabola. It crosses the x axis twice. However the first crossing is in our imaginations. It is before the kid dropped the bag, as if the bag had been thrown up from the ground instead of starting 34 meters up with an initial speed up

To determine the time it takes for the sandbag to hit the ground, we can use the equations of motion.

First, let's define our variables:
- Initial velocity of the sandbag (u) = 0 m/s (since it is dropped)
- Acceleration due to gravity (g) = 9.8 m/s^2 (assuming no air resistance)

Next, we can use the equation for displacement in terms of time:
s = ut + (1/2)at^2

In this case, the initial displacement (s) is 34m (because the balloon is 34m above the ground), the initial velocity (u) is 0 m/s, and the acceleration (a) is -9.8 m/s^2 (negative since it acts in the opposite direction to the upward velocity of the balloon).

So, we have:
34 = 0*t + (1/2)*(-9.8)*(t^2)

Simplifying the equation:
34 = -4.9*t^2

Dividing both sides by -4.9:
t^2 = -34 / -4.9
t^2 = 6.938775510204082

Taking the square root of both sides:
t ≈ √6.938775510204082

Now, here's the important part: Since we are solving for the time taken, we should only consider the positive root. Therefore, the time taken for the sandbag to hit the ground is approximately 2.63 seconds (rounded to two decimal places), not -2.41 seconds.

So, double-check your calculations to find out where the discrepancy occurred.