A sphere of mass 3kg hits a smooth horizontal floor with a speed 20 m/s at an angle of ${30}^0$ to the line of impact. The coefficient of restitution is $\frac{1}{3}.$ The impulse given to the ball by the floor is 

The floor is smooth, Hence the velocity component of the sphere parallel to the floor does not change during collision (i.e.,) In the perpendicular direction, taken positive upwards, the velocity component changes as 

$e=\frac{velocityofseparation}{velocityofapproach}=\frac{0-v\cos \beta }{u\cos \alpha -0}=\frac{v\cos \beta }{u\cos \alpha }$

$u\cos \alpha =20\times \frac{\sqrt{3}}{2}$............(1)

$v\cos \beta =eu\cos \alpha =\frac{1}{3}\times 20\times \frac{\sqrt{3}}{2}$...............(2)

Impulse, $\mathrm{J}=\mathrm{m}\left({\mathrm{v}}_{\mathrm{f}}-{\mathrm{v}}_{\mathrm{i}}\right)=3\left(\frac{1}{3}\times 20\times \frac{\sqrt{3}}{2}-\left(-20\times \frac{\sqrt{3}}{2}\right)\right)=40\sqrt{3} \mathrm{m}/\mathrm{s}$