Please see question below.
Bob can swim at a rate of 5km/h. He is in a river that is flowing at a rate of 9 km/h.
a) if bob swims upstream, what is his relative velocity to the ground?
b)if bob swims downstream, what is his relative velocity to the ground?
c) Someone decides to help Bob out of the water with a rope. bob swims across the river (perpendicular to the flow of water) in the same direction he's being pulled. The rescuer is pulling at a rate of 3 km/h. What is Bob's relative velocity to the ground?
Velocity of river = 9 km/h
Velocity of Bob = 5 km/h
a) if bob swims upstream then his velocity is opposite to that of stream so the resultant velosity will be 9-5 = 4 km/h downstream relative to the ground
b) if bob swims downstream then his velocity is in the direction of stream so the resultant velosity will be 9+5 = 14 km/h downstream relative to the ground
c) if bob swims accross the river and is pulled by a rope in the same direction by a rope at 3 km/h then his velocity accross the river is 5+3 =8 km/h and 9 km/h downstream.
His velocity relative to the ground is sqrt(8^2+9^2) = 12.04 km/h at an angle of tan(-1) (8/9) = 41.63 degrees measured from the downstream direction.