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A particle strikes a horizontal smooth floor with a velocity \( u \) making an angle \( \theta \) with the floor and rebounds with velocity \( v \) making an angle \( \phi \) with the floor. If the coefficient of restitution between the particle and the floor is \( e \), then
(1) the impulse delivered by the floor to the body is \( m u(1+e) \sin \theta \)
(2) \( \tan \phi=e \tan \theta \)
(3) \( v=u \sqrt{1-(1-e)^{2} \sin ^{2} \theta} \)
(4) the ratio of final kinetic energy to the initial kinetic energy is \( \left(\cos ^{2} \theta+e^{2} \sin ^{2} \theta\right) \)
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