A diver jumps from a platform. The height, h meters, the diver is above the water t seconds after jumping is represented by h = -16t^2 + 16t + 6.5. To the near hundredth of a second, how many seconds after jumping is the diver 2.5 meters above the water?

Rationale

1.21 seconds after jumping is when the diver is 2.5 meters above the water.

To find the time when the diver is 2.5 meters above the water, we can substitute h = 2.5 into the equation h = -16t^2 + 16t + 6.5 and solve for t. This calculation results in approximately 1.21 seconds, indicating the diver's position relative to the water.

A (2.79) YOUR ANSWER

This value represents a time that is too long for the diver to be at 2.5 meters above the water, as solving the quadratic equation provides a maximum height before descending. At 2.79 seconds, the diver is already below the water's surface.

B (1.32) YOUR ANSWER

While this time may seem plausible, it does not satisfy the height equation for 2.5 meters. Substituting 1.32 seconds into the height equation yields a height greater than 2.5 meters, indicating that the diver is still ascending rather than at the specified height.

C (2.83) YOUR ANSWER

This choice also exceeds the time calculated for the diver to reach 2.5 meters. Similar to choice A, at 2.83 seconds, the diver would have already descended below the height of 2.5 meters, making it an incorrect option.

D (1.21) CORRECT

This is the correct answer. When substituting t = 1.21 into the height equation, we find that the height equals 2.5 meters. This time accurately represents when the diver reaches that height on their descent.

Conclusion

The calculation of the diver's height above water reveals that the diver is precisely 2.5 meters high at approximately 1.21 seconds after jumping. Other choices either represent times after the diver has already descended below this height or fail to satisfy the height equation, confirming that D is the only viable solution.

A diver jumps from a platform. The height, h meters, the diver is above the water t seconds after jumping is represented by h = -16t^2 + 16t + 6.5. To the near hundredth of a second, how many seconds after jumping is the diver 2.5 meters above the water?

1.21 seconds after jumping is when the diver is 2.5 meters above the water.

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