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A particle of mass 1.0g moving with velo...

A particle of mass `1.0g` moving with velocity `v_1=3.0i-2.0j` experiences a perfectly inelastic collision with another particle of mass `2.0g` and velocity `v_2=4.0j-6.0k`. Find the velocity of the formed particle (both the vector v and its modulus), if the components of the vectors `v_1` and `v_2` are given in the SI units.

Text Solution

Verified by Experts

From conservation of momentum, for the closed system "both colliding particles"
`m_1vecv_1+m_2vecv_2=(m_1+m_2)vecv`
or, `vecv=(m_1vecv_1+m_2vecv_2)/(m_1+m_2)=(1(3veci-2vecj)+2(4vecj-6veck))/(3)=veci+2vecj-4veck`
Hence `|vecv|=sqrt(1+4+16)m//s=4*6m//s`
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Knowledge Check

  • A particle of mass 1 g moving with a velocity vecv_1=3hati-2hatj m s^(-1) experiences a perfectly in elastic collision with another particle of mass 2 g and velocity vecv_2=4hatj-6 hatk m s^(-1) . The velocity of the particle is

    A
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    D
    `6 m s^(-1)`

  • A particle of mass 1.0 g moving with a velocity vecv_1 = (3hati - 2hatj) m/s experiences a perfectly inelastic collision with another particle of mass 2.0 g and velocity vecv_2 = (4hati - 6hatj) m/s. Find the magnitude of the velocity vector vecv of the coalesced particles.

    A
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  • A ball of mass M moving with a velocity v collides perfectly inelastically with another ball of same mass but moving with a velocity v in the opposite direction. After collision

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