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

Options

A. `2.3 m s^(-1)`
B. `4.6 m s^(-1)`
C. `9.2 m s^(-1)`
D. `6 m s^(-1)`

Answer

B

Explanation

From conservation of momentum
`m_1vecv_1+m_2vecv_2=(m_1+m_2)vecv`
`1xx(3hati-2hatj)+2xx(4hatj-6hatk)=(1+2)vecv`
`implies 3hati+6hatj-12hatk=3vecv. implies vecv=hati+2hatj-4hatk`
`v=|vecv|=sqrt(1+4+16)=6.4 ms^(-1)`