#"The maximum x value can be calculated using formula:"#

#x_("max")=(v_i^2*sin 2alpha)/g#

#"where " x_("max")=100" "m" , "v_i="initial velocity"#

#alpha=45#

#2 alpha=2*45=90#

#sin 90=1#

#100=(v_i^2*sin 90)/(2*g)#

#100=v_i^2/(2.g)#

#2.g=v_i^2/100#

#"maximum height :"h_("max")=(v_i^2*sin^2 alpha)/(2g)#

#h_("max")=(v_i^2*sin^2 alpha)/(v_i^2/100)#

#h_("max")=cancel(v_i^2)*sin^2 alpha*100/cancel(v_i^2)#

#h_("max")=100*((sqrt 2)/2)^2=100*2/4=50 " m"#

#"we can write "h_("max")=1/2*g*t^2#

#50=1/2*9.81*t^2#

#100=9.81*t^2#

#t^2=100/(9.81)#

#t^2=10.19368#

#t=3.19 " s"#

#"time traveled"=2*3.19=6.38" "s#