Question

How do we determine “t” ,the seconds it takes for the ball to hit the ground?

Answer 1

Answer:

$2.64\text{ seconds}$

Explanation:

Here, we want to calculate the number of minutes it takes the ball to hit the ground

To calculate this, we have to solve the quadratic equation and record the positive t value (this is because time t, cannot be negative)

Mathematically, we have the equation to use as follows:

$t\text{ = }\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

where a is the coefficient of t^2 which is -16

b is the coefficient of t which is -15

c is the last number which is 151

Substituting the values, we have it that:

$t\text{ = }\frac{15\pm\sqrt{(-15)\placeholder{⬚}^2-4(-16)(151)}}{2(-16)}$$\begin{gathered} t\text{ = }\frac{15\pm\sqrt{9889}}{-32}\text{ = }\frac{15\pm99.44}{-32} \\ \\ t\text{ = }\frac{15+99.44}{-32}\text{ or }\frac{15-99.44}{-32} \\ \\ t\text{ = -3.58 or 2.64} \end{gathered}$

Since t cannot be negative, we have t as 2.64 seconds