Question

Can somebody help/teach me about this please?

“Suppose the equation h=-16t^2 + 35t models the altitude a football will reach t seconds after it is kicked. IS THE GIVEN VALUE POSSIBLE?”

A: h= 16 ft. B: h= 20ft.

Answer 1

A. Since we know that
`h` is the altitude a football will reach t seconds after it is kicked, we are going to replace the altitude
`h=16` in our equation and solve for
`t`. If the equation has any positive real solutions, we can conclude that the given value is possible.

We know from our problem that the given value is
`h=16`, so lets replace that value in our equation and solve for
`t`:

`h=-16t^2+35t`

`16=-16t^2+35t`

`16t^2-35t+16=0`
Solving for
`t`:

`t=1.54` or
`t=0.65`

We can conclude that the given value, h=16, is possible. In fact, the ball reaches that height two times: at
`t=0.65` and
`t=1.54`.

B. Just like before, we are going to replace the given value,
`h=20`, in our equation
`h=-16t^2+35t`, and then, we are going to solve for
`t` to check if the given value is possible. If the equation has any positive real solutions, we can conclude that the given value is possible.

`h=-16t^2+35t`

`20=-16t^2+35t`

`16t^2-35t+20=0`
Solving for
`t`:

`t= (35+i √(55))/(32)` or
`t= (35-i √(55))/(32)`

Since the equation doesn't have any real solutions, we can conclude that the given value, h=20, is not possible.