Two identical billiard balls strike a rigid wall with the same speed but at different angles, and get reflected without any change in speed, as shown in Fig. 5.6. What is (i) the direction of the force on the wall due to each ball? (ii) the ratio of the magnitudes of impulses imparted to the balls by the wall ?

Answers (1)

Let angle of ball 1=A

 Angle of ball (2)=B

 Change in velocity of ball (1) =\mathrm{V}_{\mathrm{f}}-\mathrm{V}_{\mathrm{I}}$ 
$$ (\mathrm{V} \cos \mathrm{A} \hat{\mathrm{J}}+\mathrm{V} \hat{\mathrm{i}})-(\mathrm{V} \sin \mathrm{A} \hat{\mathrm{i}}-\mathrm{V} \cos \mathrm{AJ}) $$
=2 \mathrm{V} \cos \mathrm{AJ}$
Impulse = change in momentum
$$ =2 \mathrm{MV} \cos \mathrm{AJ} $$
Direction of momentum = Normal to wall
Ratio of impulse =\frac{2 \mathrm{MV} \cos \mathrm{A}}{2 \mathrm{MV} \cos \mathrm{B}}$
=\frac{\cos A}{\cos B}$

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