Fire at the Enemy!

Recall the simplified equation for projectile motion:[br][br][center][math]y=-\frac{g}{200\cos^2\left(\theta\right)}x^2+\left(\tan\theta\right)x+y_0,[/math][br][/center]where [math]\theta[/math] denotes the angle of elevation in [b]degrees[/b], [math]y_0\ \text{m}[/math] denotes the initial height, and [math]g \approx 9.81\ \text{m}/\text{s}^2[/math] denotes the [b]gravitational constant[/b] on Earth.[br][br]We are going to fire a cannon, which is placed on the ground.
[b]Question 1. [/b]Write down the value of [math]y_0[/math].
Your cannon is located at the point with coordinates [math](0,0)[/math]. The angle of elevation is given by [math]\theta[/math], where [math]0^{\circ}<\theta<90^{\circ}[/math].
[b]Question 2. [/b]Use the GeoGebra applet above to find the range of values of [math]\theta[/math] so that your cannonball travels a horizontal distance greater than [math]8\ \text{m}[/math].
[b]Question 3. [/b]Which value of [math]\theta[/math] will give the maximum horizontal distance?
Your territory and the enemy territory is separated by a [math]3\ \text{m}[/math]-tall wall. located [math]4\ \text{m}[/math] away from you. The land to the left of the wall belongs to your territory, while the land to the right of the wall belongs to the enemy territory.
[b]Question 4. [/b]Use the GeoGebra applet to find the range of values of [math]\theta[/math] so that your cannonball enters the enemy territory.
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