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?

Rationale

Approximately 6.2 seconds is when the stone hits the ground.

To find when the stone hits the ground, we need to solve the equation h(t) = 0 using the function h(t) = -16t^2 - 60t + 984. By applying the quadratic formula, we find that the approximate time for the stone to reach the ground is 6.2 seconds.

A (4.5) YOUR ANSWER

Substituting t = 4.5 into the height function gives h(4.5) = -16(4.5)^2 - 60(4.5) + 984, which results in a positive height above ground. This indicates that at 4.5 seconds, the stone has not yet hit the ground.

B (6.2) CORRECT

This is the correct choice, as substituting t = 6.2 into the height function results in h(6.2) = 0, meaning the stone has just reached the ground.

C (8.9) YOUR ANSWER

For t = 8.9, substituting into the height function yields a negative value for h(8.9), indicating that the stone has already passed the ground level. Thus, this time is too late for the moment of impact.

D (10.4) YOUR ANSWER

At t = 10.4, substituting into the height function provides an even more negative height value. This confirms that the stone has already impacted the ground well before this time.

E (12.9) YOUR ANSWER

Similarly, for t = 12.9, the output of the height function is also negative, indicating the stone is well below ground level, validating that this time is also after the stone has hit the ground.

Conclusion

The function h(t) = -16t^2 - 60t + 984 effectively models the stone's fall, with the time t = 6.2 seconds being the moment it reaches zero height, signifying the impact with the ground. The other options represent times either before the stone hits the ground or after it has already impacted, demonstrating that 6.2 seconds is the only viable solution in this context.

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?

Approximately 6.2 seconds is when the stone hits the ground.

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