An army of armadillios is attacking Cosine Castle where the coyotes reside.
If an army must clear the 45 meter walls by 5 meters, at what angle must they set their cannons (from the horizontal) in order to fire inside the castle walls? The cannons fire cannonballs at 50 m/s.
How far away from the castle walls must they set their cannons in order to create the perfect trajectory?
Horizontal distance traveled: x
change in vertical distance: 50m
50m=50sinTheta*t-4.9 t^2
x=50costheta*t
in the second equation, solve for t in terms of x, theta
t=x/(50cosTheta)
put that into the first equation
YOu will get a final quadratic equation in terms of x, and theta. What this means, is that there are an infinite number of solutions for x and theta.Given an x, theta can be found. Given a theta, x can be found.
I have no idea what" prefect trajectory" means.