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Consider elastic collision of a particle of mass m moving with a velocity u with another particle of the same mass at rest. After the collision, the projectile and the struck particle move in directions making angles θ1 and θ2 respectively with the initial direction of motion. The sum of the angles θ1 + θ2, is:
- a)45°
- b)90°
- c)135°
- d)180°
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Consider elastic collision of a particle of mass m moving with a veloc...
Explanation:
Conservation of Momentum:
- Before the collision, the initial momentum is mu.
- After the collision, let the velocities of the particles be v1 and v2.
- Using conservation of momentum, we have: m*u = m*v1*cos(θ1) + m*v2*cos(θ2)
Conservation of Kinetic Energy:
- Since it is an elastic collision, kinetic energy is conserved.
- Using conservation of kinetic energy, we have: (1/2)*m*u^2 = (1/2)*m*v1^2 + (1/2)*m*v2^2
Angle Sum:
- Using the above two equations, we can solve for v1 and v2 in terms of u and θ1, θ2.
- Then, we can find the sum of the angles: θ1 + θ2 = 90°.
Therefore, the sum of the angles θ1 + θ2 is 90° (option B).
Conservation of Momentum:
- Before the collision, the initial momentum is mu.
- After the collision, let the velocities of the particles be v1 and v2.
- Using conservation of momentum, we have: m*u = m*v1*cos(θ1) + m*v2*cos(θ2)
Conservation of Kinetic Energy:
- Since it is an elastic collision, kinetic energy is conserved.
- Using conservation of kinetic energy, we have: (1/2)*m*u^2 = (1/2)*m*v1^2 + (1/2)*m*v2^2
Angle Sum:
- Using the above two equations, we can solve for v1 and v2 in terms of u and θ1, θ2.
- Then, we can find the sum of the angles: θ1 + θ2 = 90°.
Therefore, the sum of the angles θ1 + θ2 is 90° (option B).
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Consider elastic collision of a particle of mass m moving with a velocity u with another particle of the same mass at rest.After the collision, the projectile and the struck particle move in directions making angles θ1 and θ2 respectively with the initial direction of motion. The sum of the angles θ1 + θ2, is:a)45°b)90°c)135°d)180°Correct answer is option 'B'. Can you explain this answer?
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