Question

Can somebody help/teach me about this please?

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 $t$:
$t= \frac{35+i \sqrt{55}}{32}$ or $t= \frac{35-i \sqrt{55}}{32}$

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