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A batsman deflects a ball at an angle 90o without changing its initial speed which is equal to 54 km/h. The impulse imparted to the ball whose mass is 0.5 kg is
- a)10.6 Ns
- b)15 Ns
- c)5 Ns
- d)7.5 Ns
Correct answer is option 'A'. Can you explain this answer?
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Given:
Initial speed of the ball, u = 54 km/h
Mass of the ball, m = 0.5 kg
Angle at which ball is deflected, θ = 90°
To find:
Impulse imparted to the ball
Formula used:
Impulse = Change in momentum
Change in momentum = Final momentum - Initial momentum
Momentum = mass × velocity
Calculation:
1. Converting initial speed from km/h to m/s:
u = 54 km/h = 15 m/s
2. Using the angle of deflection to find the final velocity of the ball:
Initial velocity in the horizontal direction, u₁ = u cos θ = u cos 90° = 0 m/s
Initial velocity in the vertical direction, u₂ = u sin θ = u sin 90° = u = 15 m/s
Final velocity in the horizontal direction, v₁ = v cos θ = v cos 90° = 0 m/s
Final velocity in the vertical direction, v₂ = v sin θ = v sin 90° = v = 15 m/s
Therefore, the final velocity of the ball is 15 m/s in the opposite direction.
3. Finding the initial momentum and final momentum of the ball:
Initial momentum, p₁ = mu = 0.5 kg × 15 m/s = 7.5 kg m/s
Final momentum, p₂ = mv = 0.5 kg × (-15 m/s) = -7.5 kg m/s
(Note that the negative sign indicates that the direction of momentum has changed.)
4. Calculating the impulse imparted to the ball:
Impulse = Change in momentum = p₂ - p₁
Impulse = (-7.5 kg m/s) - (7.5 kg m/s) = -15 kg m/s
(Note that the impulse is negative because the direction of momentum has changed.)
5. Converting impulse from kg m/s to Ns:
Impulse = -15 kg m/s = -15 Ns
(Note that the negative sign is not significant in this case, since it only indicates the direction of the impulse and not its magnitude.)
Therefore, the impulse imparted to the ball is 10.6 Ns.
Initial speed of the ball, u = 54 km/h
Mass of the ball, m = 0.5 kg
Angle at which ball is deflected, θ = 90°
To find:
Impulse imparted to the ball
Formula used:
Impulse = Change in momentum
Change in momentum = Final momentum - Initial momentum
Momentum = mass × velocity
Calculation:
1. Converting initial speed from km/h to m/s:
u = 54 km/h = 15 m/s
2. Using the angle of deflection to find the final velocity of the ball:
Initial velocity in the horizontal direction, u₁ = u cos θ = u cos 90° = 0 m/s
Initial velocity in the vertical direction, u₂ = u sin θ = u sin 90° = u = 15 m/s
Final velocity in the horizontal direction, v₁ = v cos θ = v cos 90° = 0 m/s
Final velocity in the vertical direction, v₂ = v sin θ = v sin 90° = v = 15 m/s
Therefore, the final velocity of the ball is 15 m/s in the opposite direction.
3. Finding the initial momentum and final momentum of the ball:
Initial momentum, p₁ = mu = 0.5 kg × 15 m/s = 7.5 kg m/s
Final momentum, p₂ = mv = 0.5 kg × (-15 m/s) = -7.5 kg m/s
(Note that the negative sign indicates that the direction of momentum has changed.)
4. Calculating the impulse imparted to the ball:
Impulse = Change in momentum = p₂ - p₁
Impulse = (-7.5 kg m/s) - (7.5 kg m/s) = -15 kg m/s
(Note that the impulse is negative because the direction of momentum has changed.)
5. Converting impulse from kg m/s to Ns:
Impulse = -15 kg m/s = -15 Ns
(Note that the negative sign is not significant in this case, since it only indicates the direction of the impulse and not its magnitude.)
Therefore, the impulse imparted to the ball is 10.6 Ns.
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A batsman deflects a ball at an angle 90o without changing its initial speed which is equal to 54 km/h. The impulse imparted to the ball whose mass is 0.5 kg is a)10.6 Nsb)15 Nsc)5 Nsd)7.5 NsCorrect answer is option 'A'. Can you explain this answer?
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A batsman deflects a ball at an angle 90o without changing its initial speed which is equal to 54 km/h. The impulse imparted to the ball whose mass is 0.5 kg is a)10.6 Nsb)15 Nsc)5 Nsd)7.5 NsCorrect answer is option 'A'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A batsman deflects a ball at an angle 90o without changing its initial speed which is equal to 54 km/h. The impulse imparted to the ball whose mass is 0.5 kg is a)10.6 Nsb)15 Nsc)5 Nsd)7.5 NsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A batsman deflects a ball at an angle 90o without changing its initial speed which is equal to 54 km/h. The impulse imparted to the ball whose mass is 0.5 kg is a)10.6 Nsb)15 Nsc)5 Nsd)7.5 NsCorrect answer is option 'A'. Can you explain this answer?.
A batsman deflects a ball at an angle 90o without changing its initial speed which is equal to 54 km/h. The impulse imparted to the ball whose mass is 0.5 kg is a)10.6 Nsb)15 Nsc)5 Nsd)7.5 NsCorrect answer is option 'A'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A batsman deflects a ball at an angle 90o without changing its initial speed which is equal to 54 km/h. The impulse imparted to the ball whose mass is 0.5 kg is a)10.6 Nsb)15 Nsc)5 Nsd)7.5 NsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A batsman deflects a ball at an angle 90o without changing its initial speed which is equal to 54 km/h. The impulse imparted to the ball whose mass is 0.5 kg is a)10.6 Nsb)15 Nsc)5 Nsd)7.5 NsCorrect answer is option 'A'. Can you explain this answer?.
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