# Question #9a06c

Nov 7, 2017

Maximum height will be achieved when the $x$ will be half of horizontal range i.e. $\text{40 feet}$. The maximum height will be equal to $\text{20 feet}$.

#### Explanation:

In a parabolic path of a projectile motion, the max. height is achieved when

$x = \frac{\text{range}}{2}$

Now, to find the range, we can use the given equation. The value of $h \left(x\right)$ should be $0$ for two values of $x$, one for the initial point and other for the final point.

Putting $h \left(x\right) = 0$, we get

$x = 0 \mathmr{and} x = 80$

So

$\text{range = 80 feet}$

Max. Height will be achieved at

$x = \frac{80}{2} = \text{40 feet}$

Putting $x = 40$ in the equation, we get

$h \left(x\right) = \text{20 feet}$