A man can swim at a speed of 3 km/h in still water. He wants t cross a 500 m wide river flowing at 2 km/h. He flow at an angle of 120 with the river flow while swimming. A. Find the time he takes to cross the river. b.At what point on the opposite bank will he arrive?

Explanation

The Situation is shown in ure. Here `vecv_(r,g)=` velocity of the river with respect to the ground
`vecv_(m,r)=` velocity of the man with respect to the river
`vecv_(m,g)=` velocity of the man with respect to the ground.
a. We have,
`vecv_(m,g)=vecv_(m,r)+vecv_(r,g)`..........i
Hence, the velocity with respect to the ground is laong AC. Taking y- components in equation i.,
`vecv_(m,g) sin theta=3 km/h cos 3 theta^0+2 km/h cos 90^0 = (3sqrt3)/2 km/h`.
time taken to cross the river
`=(displacement along the Y-axis)/(velocity along teh Y-axis)`
`(1/2 km)/(3sqrt(3/2) km/h = 1/(3sqrt3) h`.
b. Taking x-components in equaton i,
`vecv_(m,g) cos theta= - 3km/h sin 30^0+2km/h`
`= 1/2 km/h`
displacement along the X-axis as the man crosses teh river
`=(velocity along the X-axis). (time)
`=((1 km)/(2h))xx(1/(3sqrt3) h)= 1/(6sqrt3) km`.