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?

To solve these questions, we need to understand the concept of relative velocity.

Relative velocity is the vector difference between the velocities of two objects with respect to a common reference point.

Let's solve each question step-by-step:

a) If Bob swims upstream, his relative velocity to the ground can be found by subtracting the velocity of the river from his swimming velocity.

Relative velocity (upstream) = Bob's swimming velocity - River's velocity
Relative velocity (upstream) = 5 km/h - 9 km/h
Relative velocity (upstream) = -4 km/h

Therefore, when Bob swims upstream, his relative velocity to the ground is -4 km/h.

b) If Bob swims downstream, his relative velocity to the ground can be found by adding the velocity of the river to his swimming velocity.

Relative velocity (downstream) = Bob's swimming velocity + River's velocity
Relative velocity (downstream) = 5 km/h + 9 km/h
Relative velocity (downstream) = 14 km/h

Therefore, when Bob swims downstream, his relative velocity to the ground is 14 km/h.

c) When the rescuer pulls Bob across the river perpendicular to the flow of water, Bob's swimming and the river's velocity will not affect his relative velocity to the ground. We only consider the velocity at which Bob is being pulled.

Relative velocity (rescuer pulling) = Velocity at which Bob is being pulled
Relative velocity (rescuer pulling) = 3 km/h

Therefore, when the rescuer is pulling Bob out of the water with a rope, Bob's relative velocity to the ground is 3 km/h.

To solve these questions, we need to understand the concept of relative velocity. Relative velocity is the velocity of an object observed from a reference point or another object.

a) When Bob swims upstream, his velocity relative to the ground can be calculated by subtracting the river's velocity from his swimming speed.
Bob's relative velocity to the ground (upstream) = Bob's swimming speed - River's velocity
Bob's relative velocity to the ground (upstream) = 5 km/h - 9 km/h = -4 km/h (negative sign indicates the opposite direction)

b) When Bob swims downstream, his velocity relative to the ground can be calculated by adding the river's velocity to his swimming speed.
Bob's relative velocity to the ground (downstream) = Bob's swimming speed + River's velocity
Bob's relative velocity to the ground (downstream) = 5 km/h + 9 km/h = 14 km/h

c) In this scenario, Bob is swimming across the river while being pulled in the same direction at a speed of 3 km/h. We can ignore the river's flow in this case since Bob is swimming perpendicular to it.
Bob's relative velocity to the ground (across the river) = Bob's swimming speed + Rescuer's pulling speed
Bob's relative velocity to the ground (across the river) = 5 km/h + 3 km/h = 8 km/h

So,
a) Bob's relative velocity to the ground (upstream) is -4 km/h.
b) Bob's relative velocity to the ground (downstream) is 14 km/h.
c) Bob's relative velocity to the ground (across the river) is 8 km/h.