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 find Bob's relative velocity to the ground in each scenario, we need to consider the effect of the river's flow and the rescuer's pull on his swimming speed.
a) When Bob swims upstream, his relative velocity to the ground is the difference between his swimming speed and the river's flow. In this case, since his swimming speed is 5 km/h and the river's flow is 9 km/h in the opposite direction, Bob's relative velocity to the ground is:
Relative velocity = Swimming speed - River's flow
= 5 km/h - 9 km/h (opposite direction)
= -4 km/h
Therefore, Bob's relative velocity to the ground while swimming upstream is -4 km/h. The negative sign indicates that his net motion is in the opposite direction to the intended direction of swimming.
b) When Bob swims downstream, his relative velocity to the ground is the sum of his swimming speed and the river's flow. In this case, since his swimming speed is 5 km/h and the river's flow is 9 km/h in the same direction, Bob's relative velocity to the ground is:
Relative velocity = Swimming speed + River's flow
= 5 km/h + 9 km/h (same direction)
= 14 km/h
Therefore, Bob's relative velocity to the ground while swimming downstream is 14 km/h.
c) When the rescuer helps Bob out of the water by pulling him across the river, we need to consider the combined effect of the river's flow, Bob's swimming speed, and the rescuer's pull. Since Bob swims perpendicular to the flow of water in the same direction he's being pulled, the river's flow does not affect his relative velocity to the ground.
Relative velocity = Swimming speed + Rescuer's pull
= 5 km/h + 3 km/h
= 8 km/h
Therefore, Bob's relative velocity to the ground when being pulled by the rescuer across the river is 8 km/h.