Solving Buoyancy Problem: Ball Emerges from Water Surface

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A small ball is released from a depth of 0.610 m in water, with a density 0.290 that of water, and the drag force is negligible. The initial approach using mg = mf * g was ineffective due to a mistake in density cancellation. Applying Newton's second law and kinematics led to a successful resolution of the problem. The discussion emphasizes the importance of correctly applying physical laws to solve buoyancy-related questions. Ultimately, the correct method provided the solution to how high the ball would shoot above the water surface.
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Suppose that you release a small ball from rest at a depth of 0.610 m below the surface in a pool of water. If the density of the ball is 0.290 that of water and if the drag force on the ball from the water is negligible, how high above the water surface will the ball shoot as it emerges from the water? (Neglect any transfer of energy to the splashing and waves produced by the emerging ball.)

My attempt
I tried mg = m_{f} * g

but it didn't get me anywhere

Any ideas ?
 
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Why don't you apply Newton's second law on it? Then a little kinematics will help.
 
It worked thank you :)

I tried it, but a mistake kept the density from cancelling out. I retried it after your suggestion and it worked.
 

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