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# A Batsman Deflects a Ball by an Angle of 45° Without Changing Its Initial Speed Which is Equal to 54 Km/H. What is the Impulse Imparted to the Ball? (Mass of the Ball is 0.15 Kg.) - CBSE (Science) Class 11 - Physics

ConceptNewton’s Second Law of Motion

#### Question

A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)

#### Solution 1

The given situation can be represented as shown in the following figure.

Where,

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 = vcos θ along RO

Vertical component of the initial velocity = vsin θ along PO

Horizontal component of the final velocity = vcos θ along OS

Vertical component of the final velocity = vsin 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

= mvcostheta - (- mvcos theta)

'= 2mvcos theta

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

#### Solution 2

Suppose the point O as the position of bat. AO line shows the path along which the ball stikes the bat with velocity u and OB is the path showing deflection such that angleAOB = 45^@. Now initial momentum of ball

= mu cos theta

= (0.15 xx 54 xx 1000 xx 22.5)/3600

= 0.15 xx 15 xx 0.9239 along NO

Final momentum of ball = mu cos theta along ON

Impulse = change  in momentum = mu cos theta -(-"mu"  cos theta)

= 2 mu cos theta  = 2xx0.15 xx 15 xx 0.9239 = 4.16 kg m^(-1)`

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Solution A Batsman Deflects a Ball by an Angle of 45° Without Changing Its Initial Speed Which is Equal to 54 Km/H. What is the Impulse Imparted to the Ball? (Mass of the Ball is 0.15 Kg.) Concept: Newton’s Second Law of Motion.
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