Aime F. answered • 11/23/22
Tutor
4.7
(62)
PhD in Physics (Yale), have taught Methods of Engineering Analysis
The conservation of total energy implies the initial specific kinetic energy s²/2 is converted to maximum specific potential energy gh at the trajectory apex. The decelerated height y varies below h as y = st sinθ – gt²/2, so it returns to y → 0 at a positive time t → 2s/g sinθ. The range x is unaccelerated so x = st cosθ until y → 0. Putting these facts together algebraically yields h = s²/2g = ss/2g = (x/t secθ)(gt/2 cscθ)/2g = x/2 csc2θ.
