Figure A1 Velocity of the balloon as a function of time
When the balloon is at its highest point, it stops rising and starts falling. Thus, the velocity must be passing from positive values to negative values, i.e., the velocity must be zero. Checking our graph, we see that this happens at about 21 seconds after release. In Figure A1 we repeat the velocity profile. In Figure A2 we sketch the height as a function of time. We know that the maximum height occurs when the velocity is zero.
