Question

Why doesnt the steepness of a frictionless ramp affect the velocity of the block at the bottom of the ramp?

Answer 1

As long as there are no conservative forces, and the starting height of the block is the same, the speed at the bottom will always be the same becuase of the conservation of energy.
\[E tot=KE+PE=\frac{ 1 }{ 2 }m*v^2+mgh\]
\[\Delta E tot =0=\Delta(\frac{ 1 }{ 2 }m*v^2+mgh)\]
There is no angle in the solution to v in thebottom equation