The shells fired from an artillery piece have a muzzle speed of 225 m/s, and the target is at a horizontal distance of 1.20 km. two possible angles can be used to hit the target. find the smallest angle relative to the horizontal at which the gun should be aimed? (hint: sin2θ = 2sinθcosθ)

The parametric equations for shell position are ...

... (x, y) = (v₀·cos(θ)t, -(1/2g)t²+v₀·sin(θ)t)

with conditions

... v₀ = 225 m/s

... g = 9.8 m/s²

The value of θ in the range 0–45° that makes (x, y) = (1200, 0) m for t > 0.

Solving the x equation for t, we have

Substituting this into the equation for y gives

answer: (1,3) and (-2,0) i think.