Question

20. Antonio threw a ball with an upward velocity of 6 meters per second from a height of 8meters. The formula h(x) = -4.9t^2+6t+8 describes this situation. Which is closest to the time it will take the ball to hit the ground?

Answer 1

At the time when the ball hits the ground, its height, h would be zero. Thus, we would substitute h(x) = 0 in the given equation. it becomes

- 4.9t^2 + 6t + 8 = 0

The standard form of a quadratic equation is expressed as

ax^2 + bx + c = 0

By comparing both equations, we can see that

a = - 4.9

b = 6

c = 8

We would solve for t by substituting these values into the general formula of a quadratic equation. It is expressed as

`\begin{gathered} t\text{ = }\frac{-\text{ b +- }\sqrt[]{b^2-4ac}}{2a} \\ By\text{ substituting, it becomes} \\ t\text{ = }\frac{-\text{ 6 +-}\sqrt[]{6^2-4(-\text{ 4.9 }*8)}}{2\text{ }*-\text{ 4.9}} \\ t\text{ = }\frac{-\text{ 6 +-}\sqrt[]{36\text{ + 156.8}}}{-9.8} \\ t\text{ = }\frac{-\text{ 6 + - }\sqrt[]{192.8}}{-9.8} \\ t\text{ = }\frac{-\text{ 6 +-13.89}}{-\text{ 9.8}} \\ t\text{ = }\frac{-\text{ 6 + 13.89}}{-\text{ 9.8}}\text{ or t = }\frac{-\text{ 6 - 13.89}}{-\text{ 9.8}} \\ t\text{ = - 0.81 or t = 2.03} \end{gathered}`

The time can only be positive. Thus, the time it will take the ball to hit the ground is 2.03 seconds