Iteration 2

Iteration 1

Solution

From the physics of the problem, the ball would be submerged between and ,

where

,

that is

Lets us assume

Check if the function changes sign between and

Hence

So there is at least one root between and , that is between 0 and 0.11.

The estimate of the root is

Hence the root is bracketed between and , that is, between 0.055 and 0.11. So, the lower and upper limits of the new bracket are

At this point, the absolute relative approximate error, cannot be calculated as we do not have a previous approximation.

The estimate of the root is

Hence, the root is bracketed between and , that is, between 0.055 and 0.0825. So the lower and upper limit of the new bracket is

The absolute relative approximate error, at the end of iteration #2 is

None of the significant digits are at least correct in the estimated root of because the absolute relative approximate error is greater than 5%.

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