Question

a quarterback throws an incomplete pass. the height of the football at time t is modeled by the equation $h(t) = -16t^2 + 40t + 7$. 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?

• the solution $-0.2$ s can be eliminated because time cannot be a negative value.
• the solution $-0.2$ s can be eliminated because the pass was not thrown backward.
• the solution $2.7$ s can be eliminated because the pass was thrown backward.
• the solution $2.7$ s can be eliminated because a ball cannot be in the air for that long due to gravity.

Explanation:

In the context of time for a football pass, time starts at \( t = 0 \) when the pass is thrown. Negative time values (like \(-0.2\) s) do not make sense because time cannot be negative. The solution \( 2.7 \) s is a positive time value representing when the ball hits the ground, so it is valid. The idea of the pass being thrown backward is not relevant to eliminating a negative time solution; the key reason is that time cannot be negative.

Answer:

A. The solution \(-0.2\) s can be eliminated because time cannot be a negative value.