Two paricles A and B of equal masses m are t ied with an inextensible string of length 2l. The initial distance between A and B is l. Particle A is given speed v as shown. Find the speed of particie A and B just after the string becomes taut.

Explanation

Just before string becomes taut. Just after string become taut.
`cos theta=(l)/(2l)=1/2`
Now string will apply impulse only along the string the component of the velocity A perpendicular to the string remains constatn
Thus, `v_(1)=v sin theta`
Along the string,
`Iimpliesmv_(2)`
`I=m(v cos theta-v_(2))`
`v_(2)=(v cos theta)/(2)`
Thus, speed of B is
`(vcostheta)/(2)`
Speed of A is
`sqrt((v sintheta)^(2)+((v cos theta)^(2))/(4))=v/2sqrt(1+3 sin ^(2)theta)`