Two masses nm and m, start simultaneously from the intersection of twostraight lines with velocities v and nv respectively. It is observed that the path of their centre of mass is a straight line bisecting the angle between the given straight lines. Find the magnitude of the velocity of centre of mass. [Here theta=angle between the lines]

Two masses nm and m, start simultaneously from the intersection of two

1.	Two masses nm and m, start simultaneously from the intersection of twostraight lines with velocities v and nv respectively. It is observed that the path of their centre of mass is a straight line bisecting the angle between the given straight lines. Find the magnitude of the velocity of centre of mass. [Here theta=angle between the lines]
Answer» SOLUTION :`vecv_(cm)=(m_(1)vecv_(1)+m_(1)vecv_(2))/(m_(1)+m_(2))` `vecv_(cm)=(nmvhati+mnvcosthetahati+nmv sin theta HATJ)/(m+nm)` `v_(cm)=sqrt((nmv+mnvcostheta)^(2)+(nmvsintheta)^(2))/(m(1+n))` `v_(cm)=(nmvsqrt((1+costheta)^(2)+(SINTHETA)^(2)))/(m(1+n))` `=(nvsqrt(1+cos^(2)theta+2costheta+sin^(2)theta))/((1+n))` `=((nv)/(n+1))sqrt(2costheta/2)` `v_(cm)=(2nv"cos" theta/2)/(n+1)`