Artificial intelligent assistant

How to find the range of a cannon ball? A cannon is positioned with a direction of 60 degrees between the ground and itself. (Sorry, again, for my poor English. I hope you understood that sentence.). The shooting velocity is $800{\text{m}\over \sec}$. What is its range? I didn't really understand this question. Am I asked how further the cannon ball will go before it descends? Because if so, I should I find the highest point the cannon ball get? Should I do it by differentiating? I would truly appreciate your assistance.

In the simplest model, you are working in two dimensions, with the system of equations:

$$\frac{d^2 y}{dt^2} = -g \\\ \frac{d^2 x}{dt^2} = 0 \\\ y(0)=0,y'(0)=\sin(\theta) s \\\ x(0)=0,x'(0)=\cos(\theta) s $$

where $g>0$ is acceleration due to gravity, $\theta$ is the angle of the initial velocity, and $s$ is the initial speed. Note that this model assumes no friction. When you solve you find

$$y(t)=-\frac{1}{2} gt^2 + \sin(\theta) s t \\\ x(t)=\cos(\theta) s t.$$

Now the range of the ball is the horizontal distance it travels before hitting the ground, i.e. the value of $x$ when $y=0$. Can you find this using these equations?

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