Question

I good now. thanks

Answer 1

In the figure is shown the free body diagram of the diving board. I put the diretion of the z axis going inside the page that means that all cross products of the torque that going inside the page are positive.

The sum of forces can be written as

as shown in the figure the board have no forces in x direction

the case we see is an equilibrium problem thats why the sum of the forces is equal to zero. In the equation W_b is the weight of the board and W_d is the weight of the diver. To get the sum of torques we put the reference frame in the N₂ point. The reason to choose this point is because is one of the points that don't have interest yet to study. The sum of torque is therefore

The sign of every torque depends of the reference frame and on the right hand rule. and each torques are written as

The angle theta for all cases is because the force is perpendicular to the direction of the arm lever. Replacing in the general torque sum we have

from the last equation we can solve for N3 considering that the normal force N1=Wd. it leads to

Using previous condition in the sum of forces in the y axis we have

The higher point have zero velocity, considering the energy conservation we can get the initial velocity of the diver

Using the kinematics equations we can get

considering that the x0=0 because is the origin of the coordinates the velocity components can be written as

combining both kinematic equations we will have in time

here we have a second order equation that can be solved easily. Rearreging the equation we have

Using the property

we have that the values of x are

Obviously from both solutins only we need to consider the positive one