4. 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 wedge 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 when the stone hits the ground is approximately 6.2 seconds.
To find the time when the stone hits the ground, we set the height function h(t) to zero and solve for t. The correct value of t that satisfies this equation is approximately 6.2 seconds.
A) 4.5
This option is incorrect because substituting t = 4.5 seconds into the height function h(t) results in a height above ground, indicating that the stone has not yet reached the ground.
B) 6.2
This is the correct option. Substituting t = 6.2 into the height function h(t) results in h(6.2) = 0, confirming that this is the time at which the stone hits the ground.
C) 8.9
This option is incorrect. When t = 8.9 seconds is substituted into the height function, it yields a negative height, indicating that the stone has already hit the ground before this time.
D) 10.4
This option is also incorrect. Similar to option C, substituting t = 10.4 seconds into the height function results in a negative height, which means the stone has already impacted the ground.
E) 12.9
This option is incorrect as well. Substituting t = 12.9 seconds into the height function yields a height below zero, confirming that the stone has already reached the ground well before this time.
Conclusion
The correct answer is 6.2 seconds because it is the only option that results in a height of zero when substituted into the height function, indicating that the stone has hit the ground. All other options either provide a height above ground or a negative height, indicating they do not represent the moment the stone impacts the ground.