I'm a bit confused

A basketball is thrown upwards. The height f (t), in feet, of the basketball at time t, in seconds, is given by the following function:

f (t) = - 16t2+94t+12

Which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground?

3 < t < 6

2 < t < 5

1 < t < 4

0 < t < 3

Question

Marcos Townsend

Physics

Today, 06:12

I'm a bit confused

A basketball is thrown upwards. The height f (t), in feet, of the basketball at time t, in seconds, is given by the following function:

f (t) = - 16t2+94t+12

Which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground?

3 < t < 6

2 < t < 5

1 < t < 4

0 < t < 3

+5

Answers (1)

Know the Answer?

Duncan Kidd · Answer 1

When an object is thrown upwards, it reaches a maximum height and then comes back to its starting position. If we put f (t) = 0, we can get the time the ball was thrown and the time it returned.

Solving:

-16t² + 94t + 12 = 0

t = - 0.125 and t = 6; negative time is not possible so the first solution is discarded.

The maximum height lies at the time exactly between the two times of zero displacement. Max height at

t = (-0.125 + 6) / 2 = 2.9375 s ≈ 3

3 < t < 6

Therefore, the answer is the first option.