A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s. Which solution can be eliminated and why?
Answer
A
The solution –0.2 s can be eliminated because time cannot be a negative value.
B
The solution –0.2 s can be eliminated because the pass was not thrown backward.
C
The solution 2.7 s can be eliminated because the pass was thrown backward.
D
The solution 2.7 s can be eliminated because a ball cannot be in the air for that long due to gravity.
Explanation
The equation gives two times when the football is at ground level: –0.2 seconds and 2.7 seconds. Since t represents time after the throw, a negative time is before the pass occurred and is not physically relevant. Therefore, eliminate –0.2 seconds; 2.7 seconds is the meaningful solution.
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