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?
a. what is 9-5?
b. what is 9+5?
c. draw the figure.
the perpendicular across is 5km/hr
the downstream is 9km/hr
Hmmmm. How can he swim in the same direction he is being pulled, if he is swimming at 5km/hr and the rope is pulling slower? So, I don't understand the situation. Maybe he is no longer swimming, but being pulled, but the problem says..bob swims ...
To find Bob's relative velocity to the ground in different scenarios, we need to consider the velocity of the river and the velocity at which Bob is swimming.
a) When Bob swims upstream, his swimming speed is against the current. So, to find his relative velocity to the ground, we need to subtract the river's velocity from Bob's swimming speed.
Relative velocity upstream = Bob's swimming speed - River's velocity
Relative velocity upstream = 5 km/h - 9 km/h
b) When Bob swims downstream, his swimming speed aligns with the current. So, to find his relative velocity to the ground, we need to add the river's velocity to Bob's swimming speed.
Relative velocity downstream = Bob's swimming speed + River's velocity
Relative velocity downstream = 5 km/h + 9 km/h
c) In this scenario, Bob is swimming perpendicular to the flow of water, and he is also being pulled in the same direction at a certain rate. We need to find the resulting velocity by considering the vector addition of Bob's swimming speed and the velocity at which he is being pulled.
Let's break it down into two components: the component of Bob's swimming speed perpendicular to the river's flow and the component parallel to the river's flow.
The perpendicular component is the velocity at which Bob actually moves across the river, while the parallel component is effectively cancelled out by the river's flow.
The perpendicular component is 5 km/h (Bob's swimming speed) and the parallel component is 3 km/h (the velocity at which he is being pulled).
Using the Pythagorean theorem, we can find the magnitude of the resulting velocity (relative velocity to the ground):
Resulting velocity = √(perpendicular component^2 + parallel component^2)
Resulting velocity = √(5 km/h)^2 + (3 km/h)^2
After obtaining the magnitude, we can determine Bob's relative velocity to the ground:
Relative velocity when being pulled = Resulting velocity
This gives us the answer to all three scenarios.