__Question 5.20__:

__Solution__:AO = Incident path of the ball

OB = Path followed by the ball after deflection

∠AOB = Angle between the incident and deflected paths of the ball = 45°

∠AOP = ∠BOP = 22.5° =

*θ*

Initial and final velocities of the ball =

*v*

Horizontal component of the initial velocity =

*v*cos

*θ*along RO

Vertical component of the initial velocity =

*v*sin

*θ*along PO

Horizontal component of the final velocity =

*v*cos

*θ*along OS

Vertical component of the final velocity =

*v*sin

*θ*along OP

The horizontal components of velocities suffer no change. The vertical components of velocities are in the opposite directions.

∴Impulse imparted to the ball = Change in the linear momentum of the ball

= mvCosθ - (-mvCosθ) = 2mvCosθ

Mass of the ball,

*m*= 0.15 kg

Velocity of the ball,

*v*= 54 km/h = 15 m/s

∴ Impulse = 2 × 0.15 × 15 cos 22.5° = 4.16 kg m/s

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