Final answer:
To calculate when the container hits the ground, the quadratic function h(t) = -16t² + 200 is set to h(t)=0, and solving for t yields approximately 3.54 seconds. Yet, this result does not match any of the provided options, A) 5 seconds, B) 7.5 seconds, C) 10 seconds, D) 12.5 seconds, suggesting an error with the provided options.
Step-by-step explanation:
To determine how long it takes for the container to hit the ground, we need to solve the function h(t) = -16t² + 200 for when h(t) is equal to 0. This represents the height being 0 feet, or in other words, the egg has hit the ground.
Setting the equation to zero, we get:
0 = -16t² + 200
By dividing all terms by -16, we simplify to:
0 = t² - 12.5
This is a quadratic equation. The roots of a quadratic equation can be found where the graph intersects the t-axis, which in physical problems represents time. Since time cannot be negative when considering the duration of an event, we only consider the positive root.
Solving for t, we take the square root of 12.5, which is approximately 3.54 seconds. However, this is not one of the options provided. Let's double check our calculation:
0 = -16t² + 200
t² = 200 / 16
t² = 12.5
t = √12.5
t ≈ 3.54
The closest answer to 3.54 seconds is not listed in the options (A) 5 seconds, (B) 7.5 seconds, (C) 10 seconds, (D) 12.5 seconds, which might mean there could have been a mistake in the answer options provided. Hence, there appears to be an error with either the question or the provided answer options.