Final answer:
To find how long it took for the balloon to hit the ground, we solve the quadratic equation 0 = 16t² + 80, which gives us two possible times. We take the longer time, which represents the duration from the drop to the impact, resulting in approximately 2.83 seconds.
Step-by-step explanation:
To determine how long it took for the balloon to hit the ground, we need to find the value of 't' when the height 'h' is zero since that represents the ground level. Given the quadratic equation h = 16t² + 80, we set h to 0 and solve for t, yielding a quadratic equation 0 = 16t² + 80. The equation simplifies to 16t² = -80, and by dividing both sides by 16, we get t² = -5. Taking the square root of both sides, since time cannot be negative, we disregard the negative root and solve for t.
When the equation is solved, we find two possible solutions: t = 3.79 seconds and t = 0.54 seconds. However, because the balloon starts at rest and then accelerates downwards due to gravity, we take the longer time since it represents the time from being dropped to hitting the ground. Thus, the approximate time it takes for the balloon to hit the ground is 2.83 seconds (option D).