A swimmer maintains a speed of 0.15 m/s relative to the water when swimming directly toward the opposite shore of a straight river with a current that flows at 0.75 m/s.
(a) How far downstream is the swimmer carried in 1.5 minutes?
(b) What is the velocity of the swimmer relative to an observer on shore?
This involves relative velocity, and that is about the only thing I know.
Can you help with this please? Thank you very much.
While the swimmer is trying to swim across the river he is also carried down
stream because of the velocity of the river. The swimmer has now two
velocities, 0.15 m/s which is the velocity of his swim and 0.75 m/s which is
the velocity of the river. The velocity vx = 0.75 m/s take him down stream
and the velocity vy = 0.15 m/s take him across the river. Since the velocity
of the river is a constant, the distance x the swimmer travels down stream is
given by
x = vxt = 0.75 x 1.5 x 60 = 67.5 m
(b)
The velocity of the swimmer relative to someone on the shore is the resultant
of 0.75 i and 0.15 j. The magnitude of this resultant is:
2 2 1 0.75 0.15 0.76 . m s
−
+ = .
The direction of the resultant is given by 2.0
0.75
15.0
tan = = =
x
y
θ .
Therefore, θ = tan-1 0.2 = 11.3o
.
The velocity of the swimmer relative to an observer on the shore = 0.75 m.s-
1
at an angle θ = 11.3o
measured counter clockwise with the shore.
Of course! I'd be happy to help you with this problem step-by-step.
To solve this problem, we'll need to use the concept of relative velocity. Relative velocity refers to the velocity of an object in relation to another object or reference frame.
(a) To find how far downstream the swimmer is carried in 1.5 minutes, we'll first need to convert the time to seconds. There are 60 seconds in a minute, so 1.5 minutes is equal to 1.5 x 60 = 90 seconds.
Now, we can calculate the distance using the relative velocity formula: distance = velocity × time.
The swimmer's speed relative to the water is given as 0.15 m/s. However, the swimmer is also being carried downstream by the river's current, which flows at a speed of 0.75 m/s.
To account for the downstream motion, we can subtract the speed of the river current from the swimmer's speed. So, the swimmer's effective velocity relative to the shore is 0.15 m/s - 0.75 m/s = -0.60 m/s (negative sign indicates movement downstream).
Using the formula distance = velocity × time, we can calculate the distance:
distance = (-0.60 m/s) × (90 s) = -54 m
Since distance cannot be negative in this context, we take the magnitude of the distance, which is 54 meters. Therefore, the swimmer is carried 54 meters downstream.
(b) Now let's find the velocity of the swimmer relative to an observer on the shore.
The velocity of the swimmer relative to the shore will be the sum of the swimmer's velocity relative to the water and the velocity of the water current.
Swimmer's velocity relative to the water = 0.15 m/s
Velocity of the water current = 0.75 m/s
Therefore, the velocity of the swimmer relative to an observer on the shore would be:
Velocity = Swimmer's velocity relative to the water + Velocity of the water current
Velocity = 0.15 m/s + 0.75 m/s = 0.9 m/s
So, the velocity of the swimmer relative to an observer on the shore is 0.9 m/s.
I hope this helps! Let me know if you have any further questions.
Absolutely! I can help with that. To solve this problem, we need to use the concept of relative velocity. Relative velocity is the motion of an object with respect to another object or observer.
(a) To find the distance downstream the swimmer is carried, we can use the formula: distance = velocity × time. The current of the river affects the swimmer's velocity, so we need to consider the combined velocity of the swimmer and the current. Therefore, the swimmer's effective velocity can be calculated as:
Velocity downstream = velocity of the swimmer + velocity of the current
Velocity downstream = 0.15 m/s + 0.75 m/s
Now, we can substitute the values into the distance formula:
Distance = Velocity downstream × time
Given that time = 1.5 minutes, we need to convert it to seconds:
Time = 1.5 minutes × 60 seconds/minute = 90 seconds
Now we can calculate the distance:
Distance = (0.15 m/s + 0.75 m/s) × 90 seconds
(b) To find the velocity of the swimmer relative to an observer onshore, we subtract the velocity of the current from the swimmer's velocity. This will give us:
Relative Velocity = Velocity of the swimmer - Velocity of the current
Relative Velocity = 0.15 m/s - 0.75 m/s
Now, we have the relative velocity of the swimmer with respect to an observer onshore.
I hope that helps! If you have any further questions, feel free to ask.