<p>Two inclined planes A and B have the same height but different angles of incl

Question

<p>Two inclined planes A and B have the same height but different angles of inclination with the horizontal. 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 at the bottom of&#160;inclined plane B?</p>
<p>A) It is directly proportional to the angle.</p>
<p>B) It is inversely proportional to the angle.</p>
<p>C) It is same for both planes.</p>
<p>D) There is not enough information.</p>

Explanation / Answer

Assuming the planes are frictionless, the object will start with the same potential energy at the top of both planes and wind up with the same kinetic energy at the bottom of the plane, since mechanical energy will be conserved. Therefore, the it is the same for both planes (answer C). For that matter, it doesn't matter how it gets from the top of the plane to the bottom of the plane if gravity is the only force doing work. The speed at the bottom only depends on the vertical height.

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