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Velocity after two bodies moving at right angles collide and stick together

This type of question, asked 3 times: 10 May 2024 S2, 12 May 2024 S1, 11 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    10 May 2024 S2

    38
    A mass 'MM' moving with velocity 'VV' along x-axis collides and sticks to another mass 2M2M which is moving along Y-axis with velocity '3V3V'. The velocity of the combination after collision is

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  2. Question 2

    12 May 2024 S1

    26
    A particle of mass mm moving eastward with a speed vv collides with another particle of same mass moving northward with same speed vv. The two particles coalesce after collision. The new particle of mass 2m2m will move in north east direction with a speed (in m/s)

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  3. Question 3

    11 Apr 2026 S2

    105
    A mass M moving with velocity V along X-axis collides and sticks to another mass 2M which is moving along Y-axis with velocity 3V. The velocity of the combination, after the collision is

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