Two inclined planes A and B have the same height but different angles of inclination with the horizontal. Inclined plane A has a steeper angle of inclination than inclined plane B. An object is released at rest from the top of each of the inclined planes.
How does the speed of the object at the bottom of inclined plane A compare with that of the speed at the bottom of inclined plane B?

It is the same.

Explanation:

Assuming no friction between the object and the surface, and no other external force acting on the object,  than gravity and normal force, we can say the following:

       

where ΔK = change in kinetic energy, and ΔU = change in gravitational potential energy.As ΔU = -m*g*h (being h the height of the plane), it will be the same for both inclined planes, as we are told that they have the same height.If the object starts from rest, the change in kinetic energy will be as  follows:

       

       

From (1) and (2) we see that the mass m and the height h are the  same, the speed at  the bottom of inclined plane A, will be the same as the one at the bottom of inclined plane B.

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