How Deep Will a Less Dense Ball Sink in Water?

[modulus]

Homework Statement

A ball whose density is 0.4*10³ kg/m³ falls into water from a height of 9cm. To what depth does the ball sink? Only consider bouyancy and ignore retardation due to viscocity.

(a) 9cm (b) 6cm (c) 4.5cm (d) 2.25cm

Homework Equations

Bouyant force = Volume of Body*Density of Liquid*Gravitational Acceleration

v² = u² + 2as

F = ma

Density = Mass / Volume

The Attempt at a Solution

Well, first I figured out the final velocity with which the body entered into the water using the third equation of motion (second equation stated above).

Then I figured out the retarding force acting on the body because of the bouyancy offered by the water (using the second, the first, and then the third equation stated above).

Finally I plugged in the retardation offered by bouyancy into the third equation of motion, and figured out the final answer. My answer was 3.6cm, but that is nowere in the answer choices.

Please help.

 

[Stonebridge]

In the retardation equation, did you include the fact that the ball's weight is still acting downwards on it, and that the retardation is caused by a resultant upwards force equal to buoyancy minus weight?

 

[modulus]

Umm... no I didn't. I'm stuipid, right?

Yup, well that solved the problem.

Thanks a lot.