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

When the balloon in problem 2-81 reached 500 feet, it popped and started to fall back towards the ground. The height of the balloon as it falls is modeled by the function *h*(*t*) = −16*t*^{2}+ 500, where*t*is the number of seconds since the time it popped and*h*(*t*) is the height of the balloon (in feet) above the ground. Homework Help ✎According to

*h*(*t*), when will the balloon hit the ground?Approximate the balloon's velocity at

*t*= 5 seconds.

What value of *h* represents the ground?

Velocity is slope of a distance/position graph. Since *h*(*t*) 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 *t* = 5. Use the function, *h*(*t*), 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 *t* = 5.