#"please look over the animation carefully"#
#"The initial velocity of object can be split into two components"#
#"as vertical and horizontal. "(v_x,v_y)#
#v_x=v_i*cos alpha#
#v_y=v_i*sin alpha-g*t#
#"we can find the time elapsed using the component "v_y#
#"we can write "v_y=0 " for the maximum height."#
#v_y=v_i*sin alpha-g*t=0#
#v_i*sin alpha=g*t#
#t=(v_i*sin alpha)/g#
#t_f:"represents the flaying time"#
#t_f=2*t=(2*v_i*sin alpha)/g#
#x_m=v_x*v_f#
#x_m=(v_i*cos alpha*2*v_i*sin alpha)/g#
#x_m=(v_i^2*2*sin alpha*cos alpha)/g#
#2*sin alpha*cos alpha=sin 2 alpha#
#x_m=(v_i^2*sin 2alpha)/g#
#"where:"#
#v_i=32" "m/s#
#2*alpha=pi/6*2=pi/3#
#g=9.81" "m/s^2#
#x_m=(32^2*0.866)/(9.81)#
#x_m=90.40" "m#