Two streams merge to form a river. One stream has a width of 8.3 m, depth of 3.2 m, and current speed of 2.2 m/s. The other stream is 6.8 m wide and 3.2 m deep, and flows at 2.4 m/s. If the river has width 10.4 m and speed 2.8 m/s, what is its depth?

Answers

Answer 1

Answer:

The depth of the resulting stream is 3.8 meters.

Explanation:

Under the assumption that streams are formed by incompressible fluids, so that volume flow can observed conservation:

[tex]\dot V_{1} + \dot V_{2} = \dot V_{3}[/tex] (1)

All volume flows are measured in cubic meters per second.

Dimensionally speaking, we can determine the depth of the resulting stream ([tex]h_{3}[/tex]), in meters, by expanding (1) in this manner:

[tex]w_{1}\cdot h_{1}\cdot v_{1} + w_{2}\cdot h_{2}\cdot v_{2} = w_{3}\cdot h_{3}\cdot v_{3}[/tex]

[tex]h_{3} = \frac{w_{1}\cdot h_{1}\cdot v_{1}+w_{2}\cdot h_{2}\cdot v_{2}}{w_{3}\cdot v_{3}}[/tex] (2)

[tex]v_{1}, v_{2}[/tex] - Speed of the merging streams, in meters per second.

[tex]h_{1}, h_{2}[/tex] - Depth of the merging streams, in meters.

[tex]w_{1}, w_{2}[/tex] - Width of the merging streams, in meters.

[tex]w_{3}[/tex] - Width of the resulting stream, in meters.

[tex]v_{3}[/tex] - Speed of the resulting stream, in meters per second.

If we know that [tex]w_{1} = 8.3\,m[/tex], [tex]h_{1} = 3.2\,m[/tex], [tex]v_{1} = 2.2\,\frac{m}{s}[/tex], [tex]w_{2} = 6.8\,m[/tex], [tex]h_{2} = 3.2\,m[/tex], [tex]v_{2} = 2.4\,\frac{m}{s}[/tex], [tex]w_{3} = 10.4\,m[/tex] and [tex]v_{3} = 2.8\,\frac{m}{s}[/tex], then the depth of the resulting stream is:

[tex]h_{3} = \frac{(8.3\,m)\cdot (3.2\,m)\cdot \left(2.2\,\frac{m}{s} \right) + (6.8\,m)\cdot (3.2\,m)\cdot \left(2.4\,\frac{m}{s} \right)}{(10.4\,m)\cdot \left(2.8\,\frac{m}{s} \right)}[/tex]

[tex]h_{3} = 3.8\,m[/tex]

The depth of the resulting stream is 3.8 meters.


Related Questions

TRUE or FALSE: The acceleration of projectile is 0 m/s/s at the peak of the trajectory. Identify the evidence which supports your answer.

Answers

FALSE The vertical velocity of a projectile is 0 m/s at the peak of its trajectory; but the horizontal component of the velocity at the peak is whatever the value was when first launched

The vertical acceleration of the projectile is at 0 m/s while the horizontal acceleration of the projectile at the peak of the trajectory = initial acceleration  ( i.e. statement in the question is False )

Projectile motion follows a parabolic path with x and y components of its velocity and acceleration. also the acceleration of a projectile is subject only to the acceleration due to gravity unlike other kinds of motions.

In a parabolic motion an object ( projectile ) is thrown into the air and left to move through a parabolic path under the effect of acceleration due to gravity.

Hence we can conclude that the statement is false, because horizontal acceleration of the projectile at the peak of the trajectory = initial acceleration

Learn more : https://brainly.com/question/24658194

A force of 15 N toward the WEST is applied to a 4.0 kg box. Another force of 42 N toward the EAST is also applied to the 4.0 kg box. The net force on the 4.0 kg box
is

Answers

Answer :

[tex]\implies F_1 < F_2[/tex]

[tex] \implies F_{net} = F_2 - F1[/tex]

[tex]\implies F_{net} = 42 -15[/tex]

[tex]\implies \underline{ \boxed{ F_{net} = 27 \: N}}[/tex]

The net force on the 4.0 kg box is 27 N towards EAST.

A baseball pitcher throws a fastball by spinning his arm at 27.7m/s. The ball has a mass of 0.700kg and experiences a net centripetal force of 625N. How long is the pitchers arm (the radius of the curve)?

Answers

In the historical sense, postmodern society is simply a society that occurs after the modern society. ... Many of the elements of a society like this are reactions to what the modern society stood for: industrialism, rapid urban expansion, and rejection of many past principles.

Which wave has the smallest amplitude?

I will give brainliest to the right answer.

Answers

Wave-D (the red one) has the smallest amplitude of the 4 waves on this graph.

1. Consider a 1000 kg car rounding a curve on a flat road of radius 50 m at a speed of
50 km/h (14 m/s).
a. Will the car make the turn if the pavement is dry and the coefficient of static
friction is 0.60?​

Answers

Answer:

The car will make the turn perfectly

Explanation:

Given that the centripetal force= mv^2/r

M= mass of the car

v = speed of the car

r= radius

Hence;

F = 1000 × (14)^2/50

F= 3920 N

The frictional force = μmg

μ = coefficient of static friction

m= mass

g = acceleration due to gravity

Frictional force= 0.6 × 1000× 10

Frictional force = 6000 N

The car will not skid off the curve because the frictional force is greater than the centripetal force.

write a note on unity of ant​

Answers

Answer: When a pathogen enters their colony, ants change their behavior to avoid the outbreak of disease. In this way, they protect the queen, brood and young workers from becoming ill. These results, from a study carried out in collaboration between the groups of Sylvia Cremer at the Institute of Science and Technology Austria (IST Austria) and of Laurent Keller at the University of Lausanne, are published today in the journal Science.

Explanation: search for it.

I NEED HELP ASAP!!!
which of the following causes the magnetic force between the magnet and the scrap metal?

Answers

Answer:

Alternating current at which when entered into the loop cause it to magnetize

Can a conductor be given limitless charge

Answers

Answer:

No

Explanation:

You could try to give it enough to fill all valence electrons in all of the atoms in the conductor, but practically this could not be achieved.

In a physics lab, light with a wavelength of 560 nm travels in air from a laser to a photocell in a time of 17.2 ns . When a slab of glass with a thickness of 0.810 m is placed in the light beam, with the beam incident along the normal to the parallel faces of the slab, it takes the light a time of 20.8 ns to travel from the laser to the photocell.

Required:
What is the wavelength of the light in the glass?

Answers

Answer:

Distance traveled = 3 * 10E8 * 17.2 * 10E-9 = 5.16 m

.81 / 3 * 10E8 = 2.7 * 10E-9    normal time thru glass

(20.8 - 17.2) * E10-9 = 3.6 * 10E-9   additional time due to glass

c tg = c n ta      where tg and ta are the times spent in glass and air

(Note you can also write Va = n Vg  or  D / ta = n D / tg)

n = tg / ta = 3.6 / 2.7 = 1.33 the index of refraction of the glass

Wavelength (air) = Wavelength (glass) * n

Wavelenght = 560 nm / 1.33 = 421 nm

A cylindrical water tank has a height of 20cm and a radius of 14cm. If it is filled to 2/5 of its capacity, calculate.

I. Quantity of water in the tank

II. Quantity of water left to fill the tank to its capacity.

Answers

Answer:

4.926 L Y 7.389 L

Explanation:

first you calculate the tank volume

V = π[tex](14 cm)^{2}[/tex](10 cm = [tex]12315 cm^{3}[/tex]

then you convert to liters

[tex]12315 cm^{3}[/tex] = 12.315 l

then you calculate the liters of water

2/5(12.35 l) = 4.926 l

finally we calculate the amount without water

12.315 l - 4.926 l = 7.389 l

HERE IS MORE INFORMATION ON THE SUBJECT. THEY REMOVED THE

ENGLISH SITE BUT YOU CAN USE TRANSLATOR

LINK: https://gscourses.thinkific.com/courses/fisicai

Set the initial bead height to 3.00 m. Click Play. Notice that the ball makes an entire loop. What is the minimum height required for the ball to make an entire loop

Answers

Answer:

h> 2R

Explanation:

For this exercise let's use the conservation of energy relations

starting point. Before releasing the ball

       Em₀ = U = m g h

Final point. In the highest part of the loop

       Em_f = K + U = ½ m v² + ½ I w² + m g (2R)

where R is the radius of the curl, we are considering the ball as a point body.

      I = m R²

      v = w R

we substitute

       Em_f = ½ m v² + ½ m R² (v/R) ² + 2 m g R

       em_f = m v² + 2 m g R

Energy is conserved

       Emo = Em_f

       mgh = m v² + 2m g R

       h = v² / g + 2R

 

The lowest velocity that the ball can have at the top of the loop is v> 0

      h> 2R

Automobile A and B are initially 30 m apart travelling in adjacent highway lanes at speeds VA = 14.4 km/hr., VB 23.4 km/hr. at t = 0.0. Knowing that automobile A has a constant acceleration of 0.8 m/s? and automobile B has a constant deceleration of 0.4 m/s2. Automobile A will overtake B after traveling a distance SA: A B. Side view​

Answers

Answer:

        x = 240 m

Explanation:

This is a kinematics exercise

Let's fix our frame of reference on car A

           x = x₀ₐ+ v₀ₐ t + ½ aₐ t²

         

the initial position of car a is zero

           x = 0 + v₀ₐ t + ½ 0.8 t²

for car B

          x = x_{ob} + v_{ob} t - ½ a_b t²

     

car B's starting position is 30 m

         x = 30 + v_{ob} t - ½ 0.4 t²

at the point where they meet, the position of the two vehicles is the same

         0 + v₀ₐ t + ½ 0.8 t² = 30 + v_{ob} t - ½ 0.4 t²

let's reduce the speeds to the SI system

        v₀ₐ = 14.4 km / h (1000 m / 1 km) (1h / 3600s) = 4 m / s

        v_{ob} = 23.4 km / h = 6.5 m / s

        4 t + 0.4 t² = 30 + 6.5 t - 0.2 t²

        0.2 t² - 2.5 t - 30 = 0

        t² - 12.5 t - 150 = 0

we solve the quadratic equation

       t = [tex]\frac{12.5 \pm \sqrt{12.5^2 + 4 \ 150} }{2}[/tex]

       t = [tex]\frac{12.5 \ \pm 27.5}{2}[/tex]

       t₁ = 20 s

       t₂ = -7.5 s

time must be a positive quantity so the correct result is t = 20 s

let's look for the distance

        x = 4 t + ½ 0.8 t²

        x = 4 20 + ½ 0.8 20²

        x = 240 m

I need the help
Please. I’m terrible at physics

Answers

Answer:

Explanation:

so opposite and equal , right?    forces are. soooo..

528+52= 580 N    is the force that is being exerted up on the scale

Consider two oppositely charged, parallel metal plates. The plates are square with sides L and carry charges Q and -Q. What is the magnitude of the electric field in the region between the plates

Answers

Answer:

 E = [tex]\frac{Q}{L^2 \epsilon_o}[/tex]

Explanation:

For this exercise we use that the electric field is a vector, so the resulting field is

          E_total = E₁ + E₂                      (1)

since the field has the same direction in the space between the planes

Let's use Gauss's law for the electric field of each plate

Let's use a Gaussian surface that is a cylinder with the base parallel to the plate, therefore the normal to the surface and the field lines are parallel and the angle is zero so cos 0 = 1

          Ф  = ∫ .dA = [tex]q_{int}[/tex] /ε₀

if we assume that the charge is uniformly distributed on the plate we can define a charge density

         σ = q_{int} A

             

as the field exists on both sides of the plate on the inside

          E A = A σ / 2ε₀

          E = σ / 2ε₀

           

we substitute in equation 1

         E = σ /ε₀

for the complete plate

         σ = Q / A = Q / L²

         

we substitute

         E = [tex]\frac{Q}{L^2 \epsilon_o}[/tex]

12. A car travels in a straight line with an average velocity of 80 km/h for 2.5h and then an average velocity of 40 km/h from 1.5 h (a) what is the total displacement for the 4 h trip? (b) What is the average velocity for the total trip?

Answers

Answer:

a. Total displacement = 140 km/h

b. Average velocity = 35 km/h

Explanation:

Given the following data;

Average velocity A = 80 km/h

Time A = 2.5 hours

Average velocity B = 40 km/h

Time B = 1.5 hours

a. To find the total displacement for the 4 h trip;

Total time = Time A + Time B

Total time = 2.5 + 1.5

Total time = 4 hours

Next, we would determine the displacement at each velocity.

Mathematically, displacement is given by the formula;

Displacement = velocity * time

Substituting into the formula, we have;

Displacement A = 80 * 2.5

Displacement A = 200 km/h

Displacement B = 40 * 1.5

Displacement B = 60 km/h

Total displacement = Displacement A - Displacement B

Total displacement = 200 - 60

Total displacement = 140 km/h

b. To find the average velocity for the total trip;

Mathematically, the average velocity of an object is given by the formula;

[tex] Average \; velocity = \frac {total \; displacement}{total \; time} [/tex]

Substituting into the formula, we have;

[tex] Average \; velocity = \frac {140}{4} [/tex]

Average velocity = 35 km/h

A car starting at rest accelerates at 3m/seconds square How far has the car travelled after 4s?​

Answers

Answer:

24 meters

Explanation:

Find the final velocity. 12m/s

d=[final-initial]/2×time

D=(6m/s)×4=24 m/s

This percentage of all water on the planet is salt water . 97 % 95% 93% 91%

hurry please !

Answers

Answer:

none of those are right, its technically 96.5%. so i would say 97% is your best bet because thats closest and it just rounds up :)

Explanation:

Two wires are made of the same material and have the same length but different radii. They are joined end-to- end and a potential difference is maintained across the combination. Of the following quantities that is same for both wires is
A. Potential difference
B. Electric current
C. Current density
D. Electric field

Answers

Answer:

Current

I think The choose (B)

B. Electric current

A barge is hauled along a straight-line section of canal by two horses harnessed to tow ropes and walking along the tow paths on
either side of the canal. Each horse pulls with a force of 839 N at an angle of 15° with the centerline of the canal. Find the sum of these
two forces on the barge.
answer in ___kN

Answers

Answer:

1.621 kN

Explanation:

Since each horse pulls with a force of 839 N at an angle of 15° with the centerline of the canal, the horizontal component of the force due to the first horse along the canal is F= 839cos15° N and its vertical component is F' = 839sin15° N(it is positive since it is perpendicular to the centerline of the canal and points upwards).

The horizontal component of the force due to the second horse along the canal is f = 839cos15° N and its vertical component is f' = -839sin15° N (it is negative since it is perpendicular to the centerline of the canal and points downwards).

So, the resultant horizontal component of force R = F + f = 839cos15° N + 839cos15° N = 2(839cos15°) N = 2(839 × 0.9659) = 2 × 810.412 = 1620.82 N

So, the resultant vertical component of force R' = F' + f' = 839sin15° N + (-839sin15° N) = 839sin15° N - 839sin15° N = 0 N

The magnitude of the resultant force which is the sum of the two forces is R" = √(R² + R'²)

= √(R² + 0²)  (since R' = 0)

= √R²

= R  

= 1620.82 N

= 1.62082 kN

≅ 1.621 kN

So, the sum of these  two forces on the barge is 1.621 kN

A spring of stiffness 11000 N/m is connected to a wall. The other end is attached to a block of mass 2 kg. A second spring of stiffness 12200 N/m extends between the first block and a second block of mass 2 kg. You are holding the second block with 300 N of force and everything is motionless.

Required:
How stretched is the spring connecting the first block to the wall?

Answers

Answer:

Explanation:

Let the stretch produced in first spring and second spring be x₁ and x₂ respectively. 300 N is the restoring force created in them .

k₁x₁ = k₂x₂ = 300 N .

k₁ = 11000 N/m

11000 x₁ = 300N

x₁ = 300 N / 11000

= 0.027 m

= 2.7 cm .

A small object with mass 0.20 kg swings as a pendulum on the end of a long light rope. For small amplitude of swing, the period of the motion is 3.0 s. If the object is replaced by one with mass 0.400 kg, what is the period for small amplitude of swing? (a) 1.5 s (b) 3.05 (c) 6.0 s (d) 12.0 s (e) none of the above answers

Answers

Answer:

The correct option is (e) "none of the above".

Explanation:

Given that,

A small object with mass 0.20 kg swings as a pendulum on the end of a long light rope. For small amplitude of swing, the period of the motion is 3.0 s.

If the object is replaced by one with mass 0.400 kg, then we have to find the period for small amplitude of the swing.

We know that the time period can be calculated as :

[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]

Where

l is the length

g is acceleration due to gravity

It means the time period is independent of the mass. So, if the mass is replaced by one with mass 0.400 kg, there is no effect on the time period.

After a successful experiment involving the Sun, an astrophysicist proposes a theory for how stars change during the course of their existence. Is the astrophysicist correct in doing this

Answers

Answer:

Yes

Explanation:

A scientific theory is an explanation of a natural phenomenon based on available facts. If an Astrophysicist (a scientist who studies the universe and its celestial constituents) performs several successful experiments about a natural body like the sun and tests the results of his experiment using the principles of maths and physics and they come out as true, then he can propose a scientific theory based on his findings.

Unlike a scientific law that simply states a fact, a scientific theory provides evidence and explanation to support the facts.

Wind instruments like trumpets and saxophones work on the same principle as the "tube closed on one end" that we examined in our last experiment. What effect would it have on the pitch of a saxophone if you take it from inside your house (at 76 degrees F) to the outside on a cold day when the outside temperature is 45 degrees F ?

Answers

Answer:

 f = v / 4L

the frequency of the instruments is reduced by the decrease in the speed of the wave with the temperature.

Explanation:

In wind instruments the wave speed must meet

          v = λ f

          λ = v / f

from v is the speed of sound that depends on the temperature

          v = v₀ [tex]\sqrt{1+ \frac{T [C]}{273} }[/tex]

where I saw the speed of sound at 0ºC v₀ = 331 m/s  the temperature is in degrees centigrade, we can take the degrees Fahrenheit to centigrade with the relation

            (F -32) 5/9 = C

            76ºF = 24.4ºC

            45ºF = 7.2ºC

           

With this relationship we can see that the speed of sound is significantly reduced when leaving the house to the outside

at T₁ = 24ºC               v₁ = 342.9 m / s

at T₂ = 7ºC                 v₂ = 339.7 m / s

To satisfy this speed the wavelength of the sound must be reduced, so the resonant frequencies change

              λ / 4 = L

              λ= 4L

              v / f = 4L

              f = v / 4L

Therefore, the frequency of the instruments is reduced by the decrease in the speed of the wave with the temperature.

A 650-kg elevator starts from rest. It moves upward for 3.00 s with constant acceleration until it reaches its cruis- ing speed of 1.75 m/s. (a) What is the average power of the elevator motor during this period

Answers

Answer: [tex]P=5573.43\ W[/tex]

Explanation:

Given

Mass of the elevator is [tex]M=650\ kg\\\[/tex]

Time period of ascension [tex]t=3\ s[/tex]

cruising speed [tex]v=1.75\ m/s[/tex]

Distance moved by elevator during this time

Suppose Elevator starts from rest

[tex]\Rightarrow v=u+at\\\Rightarrow 1.75=0+a(3)\\\Rightarrow a=0.583\ s[/tex]

Distance moved

[tex]\Rightarrow h=ut+0.5at^2\\\Rightarrow h=0+0.5\times 0.5833\times (3)^2\\\Rightarrow h=2.62\ m[/tex]

Gain in Potential Energy is

[tex]\Rightarrow E=mgh\\\Rightarrow E=650\times 9.8\times 2.62\\\Rightarrow E=16,720.3\ N[/tex]

Average power during this period is

[tex]\Rightarrow P=\dfrac{E}{t}\\\\\Rightarrow P=\dfrac{16,720.3}{3}\\\\\Rightarrow P=5573.43\ W[/tex]

Answer:

The power is 331.7 W.

Explanation:

mass, m = 650 kg

time, t= 3 s

initial  velocity,  u = 0 m/s

final velocity, v = 1.75 m/s

(a) The power is defined as the rate of doing work.

Work is given by the change in kinetic energy.

W = 0.5 m (V^2 - u^2)

W = 0.5 x 650 x 1.75 x 1.75 =  995.3 J

The power is given by

P = W/t = 995.3/3 = 331.7 W

A denser object will usually have a ____ index of
refraction.

Answers

Answer:

A denser object will usually have a high index of

refraction.

A denser object will usually have a high index of refraction.

What is index of refraction?

The refractive index is the ratio of the speed of light in vacuum and speed of light in any medium.

n = c/v

The density is greater for the denser medium (water, oil, mercury, etc) then the rarer medium (any gas or air).

When a light ray travels through denser medium, its velocity is reduced and the refracted ray bends towards normal.

As, the index of refraction is inversely proportional to the velocity of light in the medium, index of refraction will be high for denser object.

Thus, denser object have high index of refraction.

Learn more about index of refraction.

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Which best describes what occurs when an object takes in a wave as the wave hits it?

A. transmission
B. absorption
C. reflection
D. refraction

Answers

Answer:

B

Explanation:

ABSORPTION

A container is filled with water and the pressure at the container bottom is P. If the container is instead filled with a liquid having specific gravity 1.05, what new bottom pressure will be measured

Answers

eat ahah is when s susuehs

The following are ways to properly manage your stress except

Answers

Answer:

you should provide the options for us to answer?

What is the total kinetic energy of a 0.15 kg hockey puck sliding at 0.5 m/s and rotating about its center at 8.4 rad/s

Answers

Answer:

[tex]K=0.023J[/tex]

Explanation:

From the question we are told that:

Mass [tex]m=0.15[/tex]

Velocity [tex]v=0.5m/s[/tex]

Angular Velocity [tex]\omega=8.4rad/s[/tex]

Generally the equation for Kinetic Energy is mathematically given by

[tex]K=\frac{1}{2}M(v^2+\frac{1}{2}R^2\omega^2)[/tex]

[tex]K=\frac{1}{2}0.15(0.5^2+\frac{1}{2}(0.038)^2.(8.4rad/s^2))[/tex]

[tex]K=0.023J[/tex]

A 59.0 kg bungee jumper jumps off a bridge and undergoes simple harmonic motion. If the period of oscillation is 0.250 mins, what is the spring constant (in N/m) of the bungee cord, assuming it has negligible mass compared to that of the jumper

Answers

Answer:

The spring constant of the spring is 10.3 N/m.

Explanation:

Given that,

Mass of a bungee jumper, m = 59 kg

The period of oscillation, T = 0.25 min = 15 sec

We need to find the spring constant of the bungee cord. We know that the period of oscillation is given by :

[tex]T=2\pi\sqrt{\dfrac{m}{k}}[/tex]

Where

k is the spring constant

[tex]T^2=4\pi^2\times \dfrac{m}{k}\\\\k=4\pi^2\times \dfrac{m}{T^2}\\\\k=4\pi^2\times \dfrac{59}{(15)^2}\\\\k=10.3\ N/m[/tex]

So, the spring constant of the spring is 10.3 N/m.

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