Question

1. A ball is thrown with an initial velocity of 86 feetper second 4 feet from the ground. The functionn(t) = -16t2 + 86t + 4 represents the height, h, of theball t seconds after it was thrown. After how manyseconds will the ball hit the ground?A. 4.7 secondsB. 4.9 secondsC. 5.2 secondsD. 5.4 secondsА A

Answer 1

D. 5.4 seconds

1) Since the course of that ball is described by the function h(t) = -16t² +86t +4.

So we can sketch out:

When the ball hits the ground, we'll have to find out the 2nd root of that function since when t=0, h =4. So let's find out the roots:

`\begin{gathered} h(t)\text{ =-16t²+86t+4} \\ \Delta=(86)^2-4(-16)(4) \\ \Delta=7396+256 \\ x=\frac{-86\pm\sqrt[]{7652}}{2(-16)} \\ x_1=5.42 \\ x_2=-0.046 \end{gathered}`

3) Since just the positive answer is interesting, then we can state that the answer is D (rounded off to the nearest tenth