Question

If a certain cannon is fired from a height of 8.8 meters above the ground, at a certain angle, the height of the cannonball above the ground, h, in meters, at time, t, in seconds, is found by the function h(t)= -4.9t^2 + 30.5t + 8.8. Find the time it takes for the cannonball to strike the ground.

Answer 1

The function

`h(t)=-4.9t^2+30.5t+8.8`

Gives us the position of the cannonball measured from the ground at a time t.

When h(t)=0, the cannonball will strike the ground. Therefore,

`\begin{gathered} h(t)=0 \\ \Rightarrow-4.9t^2+30.5t+8.8=0 \end{gathered}`

Solving for t using the quadratic equation formula

`\Rightarrow t=\frac{-30.5\pm\sqrt[]{30.5^2-4(-4.9)(8.8)}}{2\cdot-4.9}=(-30.5\pm33.2074)/(-9.8)`

Then,

`\begin{gathered} \Rightarrow t_1=(-30.5+33.2074)/(-9.8)=-0.2762\ldots \\ t_2=(-30.5-33.2074)/(-9.8)=6.50075\ldots \end{gathered}`

It makes no sense that the cannonball reaches the ground before we shoot it; therefore, t_1 cannot be the answer. The only remaining possibility is t=6.5seconds

The answer is 6.5 seconds.