Question

Antonio threw a ball with an upward velocity of 6 meters per second from a height of 8 meters. The formulah(t) = -4.912 +6t + 8 describes this situation. Which is closest to the time it will take the ball to hit the ground?A) 2.03 secondsB.) 0.80 secondsC.) 4.06 secondsD.) 7.88 seconds

Answer 1

A. 2.03

Step-by-step explanation:

Formula.

`h(t)=-4.9t^2\text{ + 6t + 8}`

When h(t) = 0 means that the ball is on the ground.

So, we equal the equation to 0, and then we clear t to find it.

`0=-4.9t^2\text{ + 6t + 8}`

To solve t we have to use the quadratic formula.

`x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

a = -4.9

b = 6

c = 8

`x_1=\text{ }\frac{-6-\sqrt[]{6^2-4\cdot-4.9\cdot8}}{2\cdot-4.9}\text{ }`
`x_1=\frac{-6-\sqrt[]{13.88}}{-9.8}=2.03_{}s`

Then x2

`x_2=\frac{-6+\sqrt[]{6^2-4\cdot-4.9\cdot8}}{2\cdot-4.9}`
`x_2=\text{ }\frac{-6\text{ + }\sqrt[]{13.88}}{9.8}=\text{ -0.80 s}`

x2 It is not possible because time cannot be negative.