A river is flowing from east to west at a speed of `5m//min`. A man on south bank of river, capable of swimming `10m//min` in still water, wants to swim across the river in shortest time. He should swim

Answer

8

Explanation

If particle collide sfter time t at point P, then position of both after time t should be same both have uniform motion.
by `S=S_(0)+vxxt`
for `I^(st)` particle `S_(I)=4hat(i)+5hat(j)+(2hat(i)-3hat(j))xxt`
for `II^(nd)` particle `S_(II)=-3hat(j)+(4hat(i)+hat(j))xxt`
but `S_(I)=S_(II)`
`4hat(i)+5hat(j)+(2hat(i)-3hat(j))t=-3+(4hat(i)+hat(j))+(4hat(i)+hat(j))xxt`
`4hat(i)+8hat(j)=2hat(i)t+4hat(i)t`
by comrision along `xxDeltay`
`t=2` sec
`S_(I)=4hat(i)+5hat(j)+(2hat(i)-3hat(j))2`
`=8hat(i)-hat(j)`
`x=8 m`