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?

Rationale

Approximately 6.2 seconds is when the stone hits the ground.

To determine the time when the stone hits the ground, we need to solve the equation h(t) = 0 for the function h(t) = -16t² - 60t + 984. By applying the quadratic formula to this equation, we find that the value of t that satisfies this condition is approximately 6.2 seconds.

A (4.5) YOUR ANSWER

When substituting t = 4.5 into the function h(t), we find that the height h(4.5) remains positive, indicating that the stone has not yet reached the ground at this time. This choice is therefore too early in the fall of the stone.

B (6.2) CORRECT

This is the correct choice as substituting t = 6.2 into the function h(t) yields h(6.2) = 0, signifying that the stone has just hit the ground. This value is derived from solving the quadratic equation accurately.

C (8.9) YOUR ANSWER

For t = 8.9, when we calculate h(8.9), the height is negative, indicating that the stone has already hit the ground and is not a valid time for when the stone impacts the ground. Thus, this option is too late.

D (10.4) YOUR ANSWER

At t = 10.4, substituting into the function shows a significantly negative height, reaffirming that the stone has long since hit the ground. This choice is also invalid as it does not represent the time of impact.

E (12.9) YOUR ANSWER

Similarly, for t = 12.9, the height h(12.9) is even more negative, further confirming that the stone has already impacted the ground well before this time. Thus, this option does not represent the moment of impact.

Conclusion

In summary, the stone reaches the ground approximately at 6.2 seconds after being dropped, as indicated by the solution to the height function equating to zero. The other options either represent times before the stone hits the ground or after it has already landed, making them incorrect for this particular scenario.

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?

Approximately 6.2 seconds is when the stone hits the ground.

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