A hollow cylinder that is rolling without slipping is given a velocity of 5.0 m/s and rolls up an incline to a vertical height of 1.0 m. If a hollow sphere of the same mass and radius is given the same initial velocity, how high vertically does it roll up the incline

The hollow cylinder rolled up the inclined plane by 1.91 m

Explanation:

From the principle of conservation of mechanical energy, total kinetic energy = total potential energy

The total energy at the bottom of the inclined plane = total energy at the top of the inclined plane.

moment of inertia, I, of a hollow cylinder = ¹/₂mr²

substitute for I in the equation above;

given;

v₁ = 5.0 m/s

vf = 0

g = 9.8 m/s²

Therefore, the hollow cylinder rolled up the inclined plane by 1.91 m

i think it would be 5

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .