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When the balloon in problem 2-81 reached feet, it popped and started to fall back towards the ground. The height of the balloon as it falls can be modeled by the function , where is the number of seconds since the time it popped and is the height of the balloon (in feet) above the ground. 

  1. According to the model, when will the balloon hit the ground?

    What value of represents the ground?

  2. Approximate the balloon’s velocity at seconds.

    Velocity is slope of a distance/position graph. Since  is a parabola, we do not have the skills (yet) to find the slope on a curve. But we can approximate.

    Choose two times very close to . Use the function, , to find the balloon's height at those times. Find the slope of the line that goes through those points. This will be a good approximation of the velocity of the balloon at .