Two motor boats A and B move from same point along a circle of radius 10 m in still water. The boats are so designed that they can move only with constant speeds. The boats A and B take 16 and 8 sec respectively to complete one circle in stationary water. Now water starts flowing at `t=0` with a speed `4(m)/(s)` in a fixed direction. Find the distance between the boats after `t=8` sec.

Explanation

Since, line of action of impulse does not pass through centre of mass of the sphere, therefore, just after application of impulse, the sphere starts to move, both translationally and rotationally. Translation motion is produced by horizontal component of the impulse, while rotational motion is produced by momnt of the impulse. Let the impulse applied be `J`.
Then its horizontal coponent provides horizontal motion.
`J.cos45^@` which gives `J=4sqrt(2)kgms^(-1)`
Moment of inertial of ball about centroidal axis is
`I=2/4mR^(2)=1.6xx10^(-30kgm^(2)`
Initial angular moment of ball (about centre) =`J(Rsin45^@)`
Angular impule will change angular momentum of the ball.
`J.R sin 45^@=/_\L=(Iomega_(0)-0)`
Which gives `omega_(0)=250rads^(-1)`(clockwise)