Question

How long will it take for the ball to hit the ground? Round to the nearest hundredth.

Answer 1

Given:

`h(t)=-16t^2+95t+3`

Find-:

How long will it take for the ball to hit the ground?

Explanation-:

To hit the ground height is zero.

`h(t)=0`
`\begin{gathered} h(t)=-16t^2+95t+3 \\ \\ -16t^2+95t+3=0 \end{gathered}`

So, the time is:

`\begin{gathered} -16t^2+95t+3=0 \\ \\ \end{gathered}`

Use quadratic formula:

`\begin{gathered} ax^2+bx+c=0 \\ \\ x=(-b\pm√(b^2-4ac))/(2a) \end{gathered}`

So, the value of "t" is:

`\begin{gathered} -16t^2+95t+3=0 \\ \\ t=(-95\pm√(95^2-4(-16)(3)))/(2(-16)) \\ \\ t=(-95\pm√(9025+192))/(-32) \\ \\ t=(-95\pm96.005)/(-32) \\ \\ t=5.969,t=-0.03 \end{gathered}`

So, after 5.969 second ball to hit the ground.