46. When a stone is dropped from a certain tower, its height h above the ground, in feet, is given by the function h(t) = -16t^2 - 60t + 984, where t is the time, in seconds, since the stone was dropped. Approximately what is the value of t, in seconds, when the stone hits the ground?
Answer: B
The value of t, in seconds, when the stone hits the ground is approximately 6.2.
To determine when the stone hits the ground, we set the height function h(t) to zero and solve for t. This leads us to find that t is approximately 6.2 seconds.
A) 4.5
Choosing 4.5 seconds would imply that the stone hits the ground much earlier than it actually does. When substituting t = 4.5 into the height function h(t), the height is still positive, indicating that the stone has not yet reached the ground.
B) 6.2
This option is correct because, upon substituting t = 6.2 into the function h(t), we find that the height h(6.2) is very close to zero, confirming that this is the time at which the stone reaches the ground.
C) 8.9
If we consider 8.9 seconds, substituting this value into the height function results in a negative height, indicating that the stone has already hit the ground well before this time. Therefore, this option is not viable.
D) 10.4
Selecting 10.4 seconds also leads to a negative height when substituted into the function, which clearly shows that the stone has already impacted the ground. This option is incorrect for the context of the question.
E) 12.9
At 12.9 seconds, the height function again yields a negative result, further confirming that by this time, the stone has long since hit the ground. Thus, this option is not appropriate.
Conclusion
The correct answer is 6.2 seconds, as it accurately represents the moment when the stone reaches ground level according to the height function provided. All other options either occur before the stone hits the ground or indicate a time after the impact, making them incorrect in this context.