A vector, 5 units from the origin, along the X axis, is added to vector 2 units from the origin along the Y axis. What is the resultant vector?
a) 3î + 8ĵ
b) 5î + 2ĵ
c) 2î + 5ĵ
d) 2î + 7ĵ

Explanation

. Mass of block =2kg
and speed =2m/s
Mass of 2nd block =2kg
Let fiN/Al velocity of 2nd block =v
Using law of consevation of momentum
`2xx2=(2+2)-v`
`rarr v=1m/s`
`:.` Loss in K.E. in elastic collision
`=(1/2)xx2xx2^2-(1/2)(2+2)xx(1)^2`
`=4-2=2J`
`b. Actual loss=(Maximum loss)/2=1J`
`(1/2)xxw2xx(2)^2-(1/2)2xxv_1^2-(1/2)xx2v_2^2=1`
`rarr 4(v_1^2+v_2^2)=1`
`rarr 3-((1+e^I2)xx4)/2=1`
`rarr 2(1+e^2)=3`
`rarr 1+e^2=3/2`
`e^2=1/2`
`e=1/sqrt2`