物體已初速v被垂直上拋

s為半高..........

圖片參考：http://imgcld.yimg.com/8/n/AD01439126/o/20121212000545.jpg

物體初速v被垂直上拋,設重力加速度為g,則自拋出上升到其最大高度一半時所需時間為何?Sol: Energy eq.: mgh=mv^2/2h=v^2/2g => h1=v^2/4gh1=v*t-gt^2/2 => 0=g*t^2-2vt+2h1=g*t^2-2v*t+v^2/2g=2g^2*t^2-4gv*t+v^2t=[2gv+√(4g^2*v^2-2g^2*v^2)]/4g^2=(2gv+gv√2)/4g^2=(2+√2)v/4g..........ans