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Ok i got everything. But can please explain the assumption that system is in equilibrium and upward force = download force. When the kid is pushing the water upwards the upward force must be bigger.ok so the forces must be acting in equilibrium
upward forces= downward forces
f=P*A P is the atmospheric pressure
atmosphere is pushing the liquid upwards the weight of the liquid and reduced pressure is acting downwards
P*A=(0.9*P*A)+mg
mg=0.1P*A
mass of liquid is density*volume=p" *A*L where p" is density of liquid
p"ALg=0.1*P*A
cancel As on both sides
(P'')*L*g=0.1P
L=0.1P/(p"*g)
I think thats because we are asked to find maximum height?