Final answer:
The balloon will never hit the ground.
Step-by-step explanation:
The approximate height of the balloon at any point during its fall can be represented by the quadratic equation h = 16t^2 + 80. To find the time it takes for the balloon to hit the ground, we set h equal to 0 and solve for t. Here's how:
- Set h = 0: 16t^2 + 80 = 0.
- Divide both sides by 16: t² + 5 = 0.
- Subtract 5 from both sides: t² = -5.
- Take the square root of both sides: t = √-5.
- The square root of a negative number is not real, so it is not possible for the balloon to hit the ground in this scenario.
Therefore, the balloon will never hit the ground.