A particle travelling horizontally strikes a smooth fixed spherical surface as shown. If coefficient of restitution is e = 1/3, what should be angle θ so that it rebounds vertically.
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For a particle striking a smooth fixed sphere, the rebound direction depends on the coefficient of restitution (e) and the angle of incidence (θ). The condition for vertical rebound is that the horizontal component of velocity after impact must be zero. Since the surface is smooth, only the normal component is affected by restitution.
The relationship is given by: . Substituting e = 1/3, we get , so θ = arctan(3).
Final Answer: θ = arctan(3)