A river is a natural flowing watercourse, usually freshwater, flowing towards an ocean, sea, lake or another river. In some cases, a river flows into the ground and becomes dry at the end of its course without reaching another body of water. Small rivers can be referred to using names such as stream, creek, brook, rivulet, and rill. There are no official definitions for the generic term river as applied to geographic features, although in some countries or communities a stream is defined by its size. Many names for small rivers are specific to geographic location; examples are "run" in some parts of the United States, "burn" in Scotland and northeast England, and "beck" in northern England. Sometimes a river is defined as being larger than a creek, but not always: the language is vague.
Rivers are part of the hydrological cycle. Water generally collects in a river from precipitation through a drainage basin from surface runoff and other sources such as groundwater recharge, springs, and the release of stored water in natural ice and snowpacks (e.g., from glaciers).
Rivers and streams are often considered major features within a landscape; however, they actually only cover around 0.1% of the land on Earth. They are made more obvious and significant to humans by the fact that many human cities and civilizations are built around the freshwater supplied by rivers and streams. Most of the major cities of the world are situated on the banks of rivers, as they are, or were, used as a source of water, for obtaining food, for transport, as borders, as a defensive measure, as a source of hydropower to drive machinery, for bathing, and as a means of disposing of waste.
Potamology is the scientific study of rivers, while limnology is the study of inland waters in general.
Problem statement : I copy and paste the problem as it appears in the text. I hope am understanding its wording correctly.Diagram : The river is shown in blue. The two roads start from the crossing C and end in A and B, making angles ##60^{\circ}## and ##30^{\circ}## resectively. The longer of...
It's somewhat unusual to have a moderate earthquake up there in Alberta.
Mag 4.5, 42 km ESE of Peace River, Canada
2022-11-29 18:55:39 (UTC-08:00) 9.2 km
Mag 4.0, 40 km ESE of Peace River, Canada
2022-11-29 17:40:29 (UTC-08:00) 9.8 km
Mag 4.3, 43 km ESE of Peace River, Canada
2022-11-29...
I was hoping to explore the Calculus of Variations.
How do we prove by Calculus of Variations that the minimum time for boat crossing a river (perpendicular to the current for starters) with current ##v_r##, and boat velocity in still water ##v_b## that the path will be a straight line?
I...
I thought I could calculate the relative velocity by Pythagorean theorem there ##\sqrt{1^2+0.5^2}##
I could divide 10 meters by this value and obtain 8.95 seconds, but this is not the correct answer. Any suggestions?
From equation (3.7) , we know t = d/v_y = d / v_ABcosθ = d/ v_Asinβ
Now for time to be minimum , denominator must be maximum this implies θ=0 and β=90, but this doesn't make sense as when we try to row the boat at 0 degree with y-axis due to stream it will have a some net velocity which will...
Problem statement : While the statement is given above, I draw the given image for the problem.
Attempt : It is clear at the outset that, since the velocity of river is constant, the man will not take the same time for the forward and reverse journeys. For both journeys however, the Relevant...
v upstream = 5 - 3 =2
v of the water = 3
arccos = (2/3) = 48.19
v across the river = c^2 - a^2 = b^2
√3^2 - 2^2 = 6m/s
t = 80/6 = 13.3
can someone please point out my mistakes? am I even supposed to solve for angle like this or "perpendicular to the shores" just means that the angle is supposed...
Could I please ask for help on the last part of this question:
So, part b, I get the right time but not the right distance.
Book answers are: distance = 1/6 and time = a/V.
Here's my (faulty?) reasoning (LaTeX isn't working for me):
The boat is steered due east and so would have a velocity...
First off, to solve for this problem, I relied largely on my below drawn diagram. Forgive the poor work as this was done on a laptop.
Using the above image as reference, I came up with the below equations.
$$\frac{dy}{dx} = \frac{sin \, \theta}{1- cos \, \theta}$$
where ##cos \, \theta =...
Hi! I have a physics question I need help with.
Bob can swim at 4 m/s in still water. He wishes to swim across a river 200 m wide to a point directly opposite from where he is standing. The river flows westward at 2.5 m/s and he is standing on the South bank of the river.
a. What is the speed...
Homework Statement
You wish to row straight across a 63 meter-wide river. You can row at a steady 1.3 m/s relative to the water and the river flows at 0.57 m/s.
In what direction should you head, and how long would it take you to cross the river?
Homework EquationsThe Attempt at a Solution...
Homework Statement
A ferry boat is crossing a river that is 8.5 x 10^2 m wide.
The average velocity of the water relative to the shore is 3.8 m/s E and the average velocity of the boat relative to the water is 4.9 m/s S.
How long does it take for the boat to get across?
Homework EquationsThe...
Homework Statement
A child in danger of drowning in a river is being carried downstream by a current that has a speed of 2.35km/h. The child is 0.505km from shore and 0.780km upstream of a boat landing when a rescue boat sets out. If the boat proceeds at its maximum speed of 18.8km/h relative...
Homework Statement
Homework Equations
Minimum/Maximum occurs when the first derivative=0
The Attempt at a Solution
$$l_1^2+l_2^2=(a^2+x^2)+[b^2+(d-x)^2]=a^2+b^2+x^2+\left[ \sqrt{c^2-(b-a)^2}-x \right]^2$$
$$(l_1^2+l_2^2)'=2x+2\left[ \sqrt{c^2-(b-a)^2}-x \right](-1)$$...
Homework Statement
The water in the river moves southwest (45 degrees south of west) at 4 mi/h.
If a motorboat is traveling due east at 15 mi/h relative to the shore, determine the speed of the boat and its heading relative to the moving water.
Homework Equations
Vector summation
The Attempt...
Homework Statement
Finding the minimum time for crossing a river[/B]
how is the minimum time crossed by distance between the banks/velocity of swimmer with respect to ground as mentioned in the video?
Homework EquationsThe Attempt at a Solution
The minimum time is only possible when...
Homework Statement
A barge is loaded in a saltwater harbor and measures 3 x 20 m, sitting 0.8 m deep in the harbor. If this barge moves to freshwater, how deep will it sit?
Homework Equations
B = densitydisplaced * Vdisplaced * g
B - mg = 0
The Attempt at a Solution
So I began by solving for...
A plate is riveted with a rivet having small rod like projection over the head and the point as shown in drawing.Considering we fix the plate to a vise,and then giving torque to the Rivet Rod;What will be the Maximum Torque the rivet can withstand without getting loosened and how to calculate...
A child is in danger of drowning in the river. The river has a current of 2.5 km/hr . The child is 0.6 km from the shore. A rescue boat with speed 20.0 km/hr (with respect to the water) ,located 0.8km downstream, sets off from the shore.
What would be the optimum angle (shore -> boat ) to reach...
Homework Statement
A physics professor did daredevil stunts in his spare time. His last stunt was an attempt to jump across a river on a motorcycle. The takeoff ramp was inclined at 53 degrees, the river was 40 m. wide and the far bank was 15 m lower than the top of the ramp. The river itself...
Homework Statement
Sandra needs to deliver 20 cases of celery to the farmers' market directly east across the river, which is 32 meters wide. Her boat can move at 2.5 km/h in still water. The river has a current of 1.2 km/h flowing downstream, which happens to be moving in a southerly...
Homework Statement
You want to swim straight across a river that is 76 m wide. You find that you can do this if you swim at an angle of θ = 28° from the upstream direction at a constant rate of 1.5 m/s relative to the water. At what rate does the river flow? The angle θ is measured from the...
Homework Statement
In hot pursuit of a suspect, Agent Logan of the FBI must get directly across
a 1200m wide river in minimum time. The river's current is 0.80m/s, she can row
a boat at 1.60m/s and she can run 3.00m/s. Describe the path she should take
(rowing + running along the shore) for the...
Homework Statement
A river has a steady speed of 0.500 m/s. A student swims M upstream a distance of 1.00 km and swims back to the Q/C starting point. (a) If the student can swim at a speed of 1.20 m/s in still water, how long does the trip take? (b) How much time is required in still water...
Homework Statement
Two canoeists, A and B, live on opposite shores of a 300.0 m wide river that flows east at 0.80 m/s. A lives on the north shore and B lives on the south shore. They both set out to visit a mutual friend X who lives on the north shore at a point 200.0 m upstream from A and...
Homework Statement : River Pascal with a volume flow rate of 4.8×105L/s joins with River Archimedes, which carries 1.04×106L/s , to form the Bernoulli River. The Bernoulli River is 190 m wide and 20 m deep.[/B]Homework Equations :
What is the speed of the water in the Bernoulli River?
Express...
I have heard that rivers form from meltwater and rainwater flowing down mountains. But I know that not all rivers start near mountains. As an example the Mississippi river doesn't start near any mountains. Rather it starts at Lake Itasca which is surrounded by taiga(coniferous forest). This lake...
In the 11th chapter of Life on Kepler Bb after the whole sequence of earthquakes crumbling all the tunnels and making the homes and buildings dusty a geologist named Leon finds out that the fault line is very deep and very hot.
Leon tells all people with the power of flight to line up in...
Homework Statement
i want to know about the variation in pressure according to varo=ious depth in different water bodies like for river, lake, stream, and all with the possibility of having fresh water or salty water. (not talking about oceans) may be shore of a sea will also work.
Homework...
1. A man is on one side of a river that is 50 m wide. He is trying to get to someone directly on the other side. There is a current flowing down the stream at 2.4 m/s. His swimming speed is 3 m/s and his walking speed is 10 m/s .
What is the best angle for him to swim at to have the fastest...
What is drift in river boat problems?Is it velocity of river divided by time taken o reach the point aimed?Or velocity of river-countering velocity of swimmer or boat in the direction of boat velocity divided by time taken o reach the point aimed?In the below video ,
although the accent is...
Homework Statement
A vertical mast stands on the north bank of a river with straight parallel banks running from east to west. The angle of elevation of the top of the mast is α when measured from a point A on the south bank distant 3a to the east of the mast and β when measured from another...
Homework Statement
A river flows due north with a speed of 2.90 m/s. A man rows a boat and reaches the opposite shore right across its initial position; his velocity relative to the water is 5.50m/s. His landing point is due east relative to its initial location. The river is 1000 m wide.
a)...
The problem is:
A 230-m-wide river has a uniform flow speed of 1.4 m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 4.6 m/s with respect to the water. There is a clearing...
Homework Statement
How should you travel across a flowing river in a boat to minimize your time of travel?
A) Straight across
B) Slightly upstream
C) Slightly downstream
D) The time will be independent of how you head
Homework EquationsThe Attempt at a Solution
I thought the time would always...
Hi, I was trying to solve the following problem which was assigned to me in my Kinematics course.
I found this solution for it. I understand the concept of relative velocity of the boat to the flowing river but what I really cannot understand is the trig part, of Vb/r :
Vb/r = 5cos(theta)i -...
Homework Statement
A river is 400 feet wide and flows at 1 ft/s. A swimmer swims at 2 ft/second, straight across the river and back to where he started on the original shore. Find the time required to complete his trip.
To clarify, the turn around point is straight across the river.
(I have...
in swimmer-river physics problems ,velocity of swimmer in still water=velocity of swimmer with respect to ground OR velocity of swimmer in still water=velocity of swimmer with respect to river
which of these is correct .I am really confused.
Homework Statement
A water spider maintains an average position on the surface of a stream by darting upstream (against the current), then drifting downstream (with the current) to its original position. The current in the stream is 0.408 m/s relative to the shore, and the water spider darts...
Homework Statement
A canoe has a velocity of 0.360m/s southeast (at 315°) relative to the earth. The canoe is on a river that is flowing at 0.580m/s east relative to the earth.
Find the magnitude of the velocity v⃗ c/r of the canoe relative to the river.
Homework Equations...
Homework Statement
A canoeist wants to travel straight across a river that is 0.10km wide. However, there is a strong current moving downstream with a velocity of 3.0km/h. The canoeist can maintain a velocity relative to the water of 4.0km/h.
a) In what direction should the canoeist...
Homework Statement
Assuming no heat is transferred to or from the surroundings, how much does the temperature of a river rise in going over a 30 m falls? (assume the velocity of the water is the same above and below the falls)Homework Equations
Δl = αlΔTThe Attempt at a Solution
H = 0 and l =...
I understand that work done if we have (510,000 Kg or 5,000,000 N) of water falling 30 meters (like in a dam) would just be 5,000,000N * 30m= 150,000,000 Newton meters.
But how would one measure the work captured by a turbine for a river that say travels 50km/h. I guess assuming the same mass...
In the textbook used for my problem solving and proofs course, one of the questions asks me to develop a geometric or algebraic representation of various questions. Here is one that I'm having trouble with:
"Three cannibals and three missionaries are together on one side of the river. They...
Somehow I managed to miss an anniversary from my childhood: It was 45 years ago last Sunday that the Cuyahoga River caught fire in Cleveland, Ohio:
I was in high school at the time. My family didn’t live in the Cleveland metro area, but close enough that we mostly watched Cleveland TV...
Hi everyone,
I've been having difficulties with this problem for a while. Here is my best attempt at solving it. If there's anything wrong, I honestly can't figure it out :). I would appreciate if anyone could go over it quickly and tell me if/what I did wrong.
Homework Statement
A boat...