Show that the maximum range of a projectile in and direction is dest=cribed in the same time in which it would fall freel undr gravity throuth this distance starting from rest.

Explanation

Max. Horizontal rang ` = u^2 /g sin 2 xx 45^@ = u^2 /g`
Time of flight ` = ( 2u)/g sin 2 xx 45^2 = u^2/g`
Taking vertcal downward motion of body for time equal to time of fligh, we have:
` u=0 , a=g S= ? , t= sqrt 2 u //g`
As, ` S= ut + 1/2 at^2 = (0 xx sqrt 2 u)/g = 1/2 g xx (( sqrt 2 u)/g)^@`
`= u^2 /g = Max. H.R.`