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Two objects of identical mass begin from rest at the same height at the top of two different hills - hill A and hill B. The hills are inclined at two different angles (see diagram). The objects are released from rest and slide to the bottom; resistance forces can be considered to be negligible. The object on top of hill ____ will have the greatest speed at the bottom of the incline.

Question

Two objects of identical mass begin from rest at the same height at the top of two different hills - hill A and hill B. The hills are inclined at two different angles (see diagram). The objects are released from rest and slide to the bottom; resistance forces can be considered to be negligible. The object on top of hill ____ will have the greatest speed at the bottom of the incline.

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Solution

The question seems to be incomplete as there is no diagram provided. However, based on the information given, the speed of the objects at the bottom of the hills will depend on the height of the hills and the angles of inclination.

In the absence of air resistance and friction, the speed of an object sliding down a hill from rest is determined by the height from which it falls, not the path it takes. This is due to the conservation of energy. The potential energy the object has at the top of the hill is converted into kinetic energy as it slides down.

So, if the two hills are of the same height, the two objects should have the same speed at the bottom, regardless of the angles of the hills.

If the hills are of different heights, the object on the taller hill will have more potential energy to start with, and thus more kinetic energy (and therefore speed) when it reaches the bottom.

Without a diagram or more specific information about the heights and angles of the hills, it's impossible to definitively say which object will have the greatest speed at the bottom of the incline.

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