If we live in a world without friction, which of the following would be possible ?
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Let us examine each of the options one by one.
(1) Climb a vertical pole: The pole cannot exert a vertical force, parallel to the pole, without friction.
(2) Walk on a horizontal sidewalk: Without friction, there would be no horizontal force on you to enable you to move.
(3) Drive around a curve on a flat roadway: Since the curve is unbanked, friction is needed, or else there would be no horizontal force on the car and it would only travel in a straight line.
(4) Ride a bicycle: Without friction, the ground cannot exert the horizontal force on the wheels necessary for traction.
Hence we are left with jumping into the air, so that is the answer.