At what angle must a rifle be fired if it is to hit a target at the same level 150 m away dead center? The initial speed of the bullet is 450m/s
time in air: 450cosTheta*time=150
time in air= 1/3cosTheta second
but in the vertical
time in air is found by
hf=hi+vi'*t -4.9t^2 or
t=sqrt(450sinTheta/4.9)
set the two time equal
sqrt(450sinTheta/4.9)=1/3cosTheta
and you have the solution with a little trig. Remember
cos^2 X= 1-sin^2 x ...and the quadratic equation