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Home > CALC > Chapter 2 > Lesson 2.3.2 > Problem 2-119


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 is 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 , 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 .