A lawn sprinkler is constructed in such a way that $\frac{d\theta}{dt}$ is constant, where $\theta$ ranges between 45° and 135° (see figure). The distance the water travels horizontally is $x = \frac{v^2\sin(2\theta)}{32}$, $45^\circ \le \theta \le 135^\circ$ where the constant $v$ is the speed of the water.
Find $\frac{dx}{dt}$
$\frac{dx}{dt} = (\text{_____})\frac{d\theta}{dt}$
What part of the lawn receives the most water?
$\circ$ the inner part
$\circ$ the outer part
$\circ$ the lawn sprinkler waters evenly
