a vessel field with water is kept on a fricionless surface and an orifice is created at the depth, the orifice area is 100 times smaller than the vessel area. find the acceleration of vessel at time t=0,at time t=t and distance travelled as water finishes?

Dear student

The parameters (acceleration, force on vessel etc) would be time dependent because the depth in the vessel decreases as the time will progress. So, here, we need to form the differential equations and integrate them to get the distance travelled.

Assume time dt and in that time, take fall of level = dh.
Use, reduction in volume = Water out of orifice

A_vdh = (√2gh ) A_odt

Thanks