Problem about centroids II

The asking problem: Show that when the distance h is selected to maximize the distance Y from line BB' to the centroid of the shaded area, we also have Y=h. Note: The Y is relating to the centroid Y of the area. The drawing is in word97 format for PC and not for MAC. My problem is I don't know how can I demonstrate this. Can you explain to me how??

Problems about centroids III

Asking problem: Divide the parabolic spandrel shown into five vertical sections and determinate by approximate means the x coordinate of its centroids; approximate the spandrel by rectangles of the form bdd'b'. Note: The drawing file is in word97 format for PC and not for MAC. My question is how can I determine the area of each rectangular section?? The answer of this problem is: X=0.7424a

Working with conservation of momentum and collisions.

On a frictionless ice, a block whose mass is A= 6 kg is sliding toward +x with a velocity VA= 8 m/sec, when it collides in a non-elastic collision with a block of mass B= 4 kg moving at an unknown velocity VB. After collision the joined blocks move with momentum P= 84 i + 48 j where i and j are unit vectors. a. Find PB the original momentum of mass B before collision. b. Find VB the velocity of mass B before collision using unit vectors.

Block sliding on a sphere

A small block slides from rest from the top of a frictionless sphere of radius R. How far below the top of the sphere does the block lose contact with the sphere? The sphere does not move. Gravity is acting on the block.

True and false question about the relationship between gravitational and kinetic energy.

You drop a ball (initially at rest) from a height of 12 meters above the ground. You can neglect air resistance. Which statements are true about this situation? (Give ALL correct answers) A) The kinetic energy and the gravitational potential energy of the ball are equal when the ball is at a height of 6 meters B) The kinetic energy of the ball is 1/3 of the total energy when the ball is at a height of 8 meters C) The maximum value of kinetic energy occurs when the ball is at a height of 0 meters D) The sum of KE + PE stays the same as the ball falls E) The kinetic energy of the ball will be twice the gravitational potential energy when the ball is at a height of 4 meters.