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An ice skater of 60kg wears a helmet of 10kg. while moving 2m/s velocity, he throw helmet in a perpendicular direction with 5 m/s. Find his new a) velocity in original direction b)velocity in perpendicular direction c ) resultant velocity?
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An ice skater of 60kg wears a helmet of 10kg. while moving 2m/s veloci...
Solution:
Given,
Mass of ice skater, m1 = 60 kg
Mass of helmet, m2 = 10 kg
Initial velocity of ice skater, u1 = 2 m/s
Initial velocity of helmet, u2 = 0 (since it was at rest)
Final velocity of helmet, v2 = 5 m/s
### Conservation of Momentum
When the ice skater throws the helmet, the system of ice skater and helmet is isolated from the external world. Therefore, the total momentum of the system before throwing the helmet is equal to the total momentum of the system after throwing the helmet. This is known as the principle of conservation of momentum.
### Calculation of velocity of ice skater after throwing the helmet
Let the final velocity of ice skater be v1.
Using the principle of conservation of momentum, we can write:
m1u1 + m2u2 = m1v1 + m2v2
Substituting the given values, we get:
60 × 2 + 10 × 0 = 60v1 + 10 × 5
=> v1 = 0.33 m/s
Therefore, the velocity of ice skater after throwing the helmet is 0.33 m/s.
### Calculation of velocity of helmet in perpendicular direction
Let the velocity of helmet in perpendicular direction be v3.
Since there is no external force acting on the system in the perpendicular direction, the principle of conservation of momentum can be applied in this direction as well.
Using the principle of conservation of momentum, we can write:
m1u1 = m1v1 + m2v3
Substituting the given values, we get:
60 × 2 = 60 × 0.33 + 10v3
=> v3 = 3.34 m/s
Therefore, the velocity of helmet in perpendicular direction is 3.34 m/s.
### Calculation of resultant velocity of ice skater after throwing the helmet
Let the resultant velocity of ice skater after throwing the helmet be v.
Using the Pythagorean theorem, we can write:
v² = v1² + v3²
Substituting the given values, we get:
v² = 0.33² + 3.34²
=> v = 3.36 m/s
Therefore, the resultant velocity of ice skater after throwing the helmet is 3.36 m/s.
Explanation:
When the ice skater throws the helmet, the system of ice skater and helmet is isolated from the external world. Therefore, the total momentum of the system before throwing the helmet is equal to the total momentum of the system after throwing the helmet. Using the principle of conservation of momentum, we can calculate the velocity of ice skater after throwing the helmet, which is 0.33 m/s. We can also calculate the velocity of helmet in perpendicular direction, which is 3.34 m/s, using the same principle. Finally, using the Pythagorean theorem, we can calculate the resultant velocity of ice skater after throwing the helmet, which is 3.36 m/s.
Given,
Mass of ice skater, m1 = 60 kg
Mass of helmet, m2 = 10 kg
Initial velocity of ice skater, u1 = 2 m/s
Initial velocity of helmet, u2 = 0 (since it was at rest)
Final velocity of helmet, v2 = 5 m/s
### Conservation of Momentum
When the ice skater throws the helmet, the system of ice skater and helmet is isolated from the external world. Therefore, the total momentum of the system before throwing the helmet is equal to the total momentum of the system after throwing the helmet. This is known as the principle of conservation of momentum.
### Calculation of velocity of ice skater after throwing the helmet
Let the final velocity of ice skater be v1.
Using the principle of conservation of momentum, we can write:
m1u1 + m2u2 = m1v1 + m2v2
Substituting the given values, we get:
60 × 2 + 10 × 0 = 60v1 + 10 × 5
=> v1 = 0.33 m/s
Therefore, the velocity of ice skater after throwing the helmet is 0.33 m/s.
### Calculation of velocity of helmet in perpendicular direction
Let the velocity of helmet in perpendicular direction be v3.
Since there is no external force acting on the system in the perpendicular direction, the principle of conservation of momentum can be applied in this direction as well.
Using the principle of conservation of momentum, we can write:
m1u1 = m1v1 + m2v3
Substituting the given values, we get:
60 × 2 = 60 × 0.33 + 10v3
=> v3 = 3.34 m/s
Therefore, the velocity of helmet in perpendicular direction is 3.34 m/s.
### Calculation of resultant velocity of ice skater after throwing the helmet
Let the resultant velocity of ice skater after throwing the helmet be v.
Using the Pythagorean theorem, we can write:
v² = v1² + v3²
Substituting the given values, we get:
v² = 0.33² + 3.34²
=> v = 3.36 m/s
Therefore, the resultant velocity of ice skater after throwing the helmet is 3.36 m/s.
Explanation:
When the ice skater throws the helmet, the system of ice skater and helmet is isolated from the external world. Therefore, the total momentum of the system before throwing the helmet is equal to the total momentum of the system after throwing the helmet. Using the principle of conservation of momentum, we can calculate the velocity of ice skater after throwing the helmet, which is 0.33 m/s. We can also calculate the velocity of helmet in perpendicular direction, which is 3.34 m/s, using the same principle. Finally, using the Pythagorean theorem, we can calculate the resultant velocity of ice skater after throwing the helmet, which is 3.36 m/s.
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An ice skater of 60kg wears a helmet of 10kg. while moving 2m/s velocity, he throw helmet in a perpendicular direction with 5 m/s. Find his new a) velocity in original direction b)velocity in perpendicular direction c ) resultant velocity?
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An ice skater of 60kg wears a helmet of 10kg. while moving 2m/s velocity, he throw helmet in a perpendicular direction with 5 m/s. Find his new a) velocity in original direction b)velocity in perpendicular direction c ) resultant velocity? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An ice skater of 60kg wears a helmet of 10kg. while moving 2m/s velocity, he throw helmet in a perpendicular direction with 5 m/s. Find his new a) velocity in original direction b)velocity in perpendicular direction c ) resultant velocity? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ice skater of 60kg wears a helmet of 10kg. while moving 2m/s velocity, he throw helmet in a perpendicular direction with 5 m/s. Find his new a) velocity in original direction b)velocity in perpendicular direction c ) resultant velocity?.
An ice skater of 60kg wears a helmet of 10kg. while moving 2m/s velocity, he throw helmet in a perpendicular direction with 5 m/s. Find his new a) velocity in original direction b)velocity in perpendicular direction c ) resultant velocity? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An ice skater of 60kg wears a helmet of 10kg. while moving 2m/s velocity, he throw helmet in a perpendicular direction with 5 m/s. Find his new a) velocity in original direction b)velocity in perpendicular direction c ) resultant velocity? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ice skater of 60kg wears a helmet of 10kg. while moving 2m/s velocity, he throw helmet in a perpendicular direction with 5 m/s. Find his new a) velocity in original direction b)velocity in perpendicular direction c ) resultant velocity?.
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