"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