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The vector 40î + 30ĵ is added to a vecto...

The vector 40î + 30ĵ is added to a vector. The result gives 15î + 3ĵ as the answer. The unknown vector is _____
a) -25î – 27ĵ
b) 25î + 27ĵ
c) -25î + 27ĵ
d) 25î – 27ĵ

Text Solution

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Mas of 1st ball =m
and speed =v
Mass of 2nd ball =m
Let fiN/Al velocities of 1st and 2nd ball are `v_1 and v_2` respectively
Using law of conservation of momentum
`m(v_1+v_2)=mv`……i
`rarr v_1+v_2=v`…………ii
`also v_1-v_2=ev`
Given that fiN/Al K.E.`=3/4 initial K.E.
`rarr 1/2 mv_1^2+1/2mv_2^2=3/4xx1/2mv^2`
`rarr v_1^2+v_2^2=3/4v^2`
`rarr v_1^2+v_2^2=3/4v^2`
`rarr ((v_1+v_2)^2+(v_1-v_2)^2)/2=3/4v^2`
`rarr ((1+e^2)v^2)/2=3/4v^2`
rarr 1+e^2=(3/2)`
`rarr e^2=1/2`
`-e=1/sqrt2`
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