The angular elevation of an enemies position on a hill of height 'h' is `alpha`. Show that in order to hit a shell on it, the initial velocity 'u' of projection should not be less than `sqrt((gh (1+ cosec alpha))` where g is acceleration due to gravity.

Find the time required for a cylindrical tank of radius r and height H to empty through a round hole of area a at the bottom. The flow through the hole is according to the law v(t)=ksqrt(2gh(t)) , where v(t) and h(t) , are respectively, the velocity of flow through the hole and the height of the water level above the hole at time t , and g is the acceleration due to gravity.

A hemi-spherical tank of radius 2 m is initially full of water and has an outlet of 12c m^2 cross-sectional area at the bottom. The outlet is opened at some instant. The flow through the outlet is according to the law v(t)=0.6sqrt(2gh(t)), where v(t) and h(t) are, respectively, the velocity of the flow through the outlet and the height of water level above the outlet and the height of water level above the outlet at time t , and g is the acceleration due to gravity. Find the time it takes to empty the tank.