Question

A ball is thrown in the air. The relationship between the time the ball is in the air in seconds (t) and the height of the ball in feet above the ground (h) is represented by h=-16t² + 46t + 6. How many seconds will it take for the ball to hit the ground?

Explain.

Answer 1

Check the picture below.

so the seconds will be the value of "t" when h = 0, so

`\stackrel{h}{0}=-16t^2+46t+6\implies 0=2(-8t^2+23t+3)\implies 0=-8t^2+23t+3 \\\\\\ 8t^2-23t-3=0\implies (t-3)(8t+1)=0\implies t= \begin{cases} -(1)/(8)&\bigotimes\\\\ 3&\checkmark \end{cases}`

notice, the seconds value cannot be negative, so -1/8 is not a plausible value.