Acceleration word problem help :/

[kholdstare121]

acceleration/velocity word problem help!

The problem is:
A hot air balloon is ascending straight up at a constant speed of 7.0 m/s. when the balloon is 12.0 m above the ground, a gun fires a pellet straight up from ground level with an initial speed of 30.0 m/s. Along the paths of the balloon and the pellet, there are two places where each of them has the same altitude at the same time. How far above ground level are these places?

I've been stuck on this problem for hours.
I started out using the equation d=Vi*t+1/2*a*t^2 for both the balloon and the pellet, then set them equal
but I run into problems of where to include the 12.0m at.
Ugh...where do I start?

 

[Hootenanny]

You should use the full equation;

$$d = d_{i} + v_{i}t + \frac{1}{2}at^{2}$$

Where d_i is the intial position. Set the displacements equal to each other and solve for t. Does that make sense?

 

[kholdstare121]

You should use the full equation;

$$d = d_{i} + v_{i}t + \frac{1}{2}at^{2}$$

Where d_i is the intial position. Set the displacements equal to each other and solve for t. Does that make sense?

we've never learned that equation


Edit*
But I had the same idea, I just am confused about the balloon's displacement
Would it be $$12m+7.0m/s*t$$??

 

[kholdstare121]

The final equation I end up getting is 0=-4.9m/s^2*t^2-7.0m/s*t-12m
When I solve that using the quadratic formula I get the squareroot of a negative number.
What am I doing wrong?

 

[Hootenanny]

But I had the same idea, I just am confused about the balloon's displacement
Would it be $$12m+7.0m/s*t$$??

That is spot on, so you should have;

$$7t + 12 = 30t - 4.905t^{2}$$

Correct?