Question

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 1

ANSWER

The solution that can be eliminated is $- 0.2s$ because time does not read backwards and hence can never he negative.

EXPLANATION

The reason why we eliminate the solution of
$- 0.2s$
is that time cannot be negative.

While the ball is still in the hands of the quarterback, the time is
$t = 0$

As soon as he throws the ball, the time starts reading forward.

When
$h(t) = 0$
the ball is no longer in the air. The ball took some time to travel through space before landing.

Time does not read backwards, that is the reason why the time taken for the ball to land cannot be negative.

Answer 2

-0.2s

You cannot have a negative amount of time.