Acceleration word problem help :/

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A hot air balloon ascends at a constant speed of 7.0 m/s from 12.0 m above ground when a pellet is fired upwards at 30.0 m/s. To find the points where both the balloon and pellet reach the same altitude, the equation d = d_i + v_i*t + 1/2*a*t^2 is suggested for both objects. The balloon's displacement is correctly expressed as 12 m + 7.0 m/s * t, while the pellet's displacement includes its initial speed and acceleration due to gravity. The final equation to solve is 7t + 12 = 30t - 4.905t^2, which leads to a quadratic equation. Properly solving this will yield the altitudes where both the balloon and pellet are at the same height.
kholdstare121
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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?
 
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You should use the full equation;

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

Where di is the intial position. Set the displacements equal to each other and solve for t. Does that make sense?
 
Hootenanny said:
You should use the full equation;

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

Where di 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 :confused:
:frown:

Edit*
But I had the same idea, I just am confused about the balloon's displacement
Would it be 12m+7.0m/s*t??
 
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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?
 
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kholdstare121 said:
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?
 
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