Question

How many seconds does it take until the ball hits the ground ?

Answer 1

Given:

The quadratic model of the ball is given as:

`h(t)=-16t^2+104t+56`

Required:

Find the time when it takes to hit the ground.

Step-by-step explanation:

When the ball hits the ground then h(t)=0.

`\begin{gathered} -16t^2+104t+56=0 \\ -8(2t^2-13t-7)=0 \\ 2t^2-13t-7=0 \end{gathered}`

Solve the quadratic equation by using the middle term splitting method.

`\begin{gathered} 2t^2-14t+t-7=0 \\ 2t(t-7)+1(t-7)=0 \\ (t-7)(2t+1)=0 \\ t=7,-(1)/(2) \end{gathered}`

Since time can not be negative.

So t = 7 sec

Final Answer:

The ball will take 7 sec to hits the ground.