According to the conservation of energy, how does the speed of the block at the bottom of the ramp relate to its height?

The correct response highlights the relationship established by the conservation of energy principles. When an object, such as a block, rolls down a ramp, its potential energy at a certain height is converted into kinetic energy as it descends.

At the top of the ramp, the block possesses gravitational potential energy given by the equation ( PE = mgh ), where ( m ) is the mass of the block, ( g ) is the acceleration due to gravity, and ( h ) is the height from which it descends. As the block moves down the ramp, this potential energy gets converted into kinetic energy, defined as ( KE = \frac{1}{2} mv^2 ).

When the block reaches the bottom of the ramp, all the potential energy has been transformed into kinetic energy, assuming no energy losses due to friction or air resistance. The conservation of energy principle dictates that the total mechanical energy remains constant, leading to the equation:

[ mgh = \frac{1}{2} mv_b^2 ]

In this equation, ( v_b ) is the speed of the block at the bottom of the ramp. By simplifying this equation—cancelling out the mass and rearranging—we arrive at the