A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground ? (b) With what speed does it hit the ground ?

Explanation

To solve the problem of the hot-air balloon and the dropped package, we can break it down into two parts:

### Part (a): Time taken for the package to reach the ground

1. **Understanding the motion**: The package is initially moving upward with the balloon at a speed of 12 m/s when dropped. It will first ascend until its velocity reaches 0 m/s, then it will descend to the ground.

2. **Calculate the time to reach the maximum height (t1)**:
- Initial velocity (u) = 12 m/s (upward)
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