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tino4ka555 [31]
4 years ago
11

A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through a

n angle θ . How should θ be chosen so that the gutter will carry the maximum amount of water?
Physics
1 answer:
GarryVolchara [31]4 years ago
7 0

Answer:

60

Explanation:

The volume of the water carried will be proportional to the cross-sectional area. The cross-section is a trapezoid with height 10sint, where t represents theta. The top of the trapezoid is 10+(2)(10cost), i.e. 10 + 20cost. The base of the trapezoid is 10.

Area of trapezoid = (average of bases) times (height)

= ([10 + (10 +20cost)] / 2 ) 10 sint

= (10 + 10cost)(10sint)

= 100sint + 100sintcost, call this A(t). You need to maximize. So differentiate and set equal to zero.

dA/dt = -100sin(t)^2+100cos(t)+100cos(t)^2 = 0, divide by 100:

-sin(t)^2 + cos(t) + cos(t)^2 = 0, replace sin^2 by 1-cos^2

2cos(t)^2 + cos(t) - 1 = 0, factor

(1+cos(t))(2cos(t)-1)=0, so  

cos(t)=1, t=0 that give a min (zero area) not a max, or

cos(t) = 1/2, so t=60 degrees. This gives the max.

You might be interested in
A car starts from rest with an acceleration of 5.0 m / s² and travels a distance of 1.0 km. What is the speed value of this car?
Pepsi [2]

Answer:

100 m/s

Explanation:

We'll begin by converting 1 km to m. This can be obtained as follow:

1 km = 1000 m

Finally, we shall determine the final velocity of the car. This can be obtained as follow:

Initial velocity (u) = 0 m/s

Acceleration (a) = 5.0 m/s²

Distance (s) = 1000 m

Final velocity (v) =?

v² = u² + 2as

v² = 0² + (2 × 5 × 1000)

v² = 0 + 10000

v² = 10000

Take the square root of both side

v = √10000

v = 100 m/s

Therefore, the speed value of the car is 100 m/s.

5 0
3 years ago
Of the numbers 0.0034 m, 45.6 m, and 1234 m, which is the most precise?
julia-pushkina [17]

Answer:

The most precise is 0.0034 m ⇒ 1st answer

Explanation:

<em>Lets revise the meaning of precise</em>

Precision is referred as the closeness of two measurements to one

another.

Highest number with significant digit is the most precise

Ex: <em>Highest significant </em>of optical instrument is the Wavelength of visible (red)

light = 0.00006 cm

Hence the <em><u>most precise</u></em> device for measuring length is the given optical

instrument

The difference between accuracy and precise

<em>Accuracy</em> is how close a value is to its true value

<em>Precision</em> is how repeatable a measurement is

We have three numbers

0.0034 m, 45.6 m, and 1234 m

The least precise is 1234 m

The most precise is 0.0034 m

4 0
3 years ago
Read 2 more answers
Question 6 (10 points)
horsena [70]

Answer:

a= g = - 9.81 m/s2.

The following equations will be helpful:

a = (vf - vo)/t d = vot + 1/2 at2 vf2 = vo2 + 2ad

When you substitute the specific acceleration due to gravity (g), the equations are as follows:

g = (vf - vo)/t d = vot + 1/2 gt2 vf2 = vo2 + 2gd

If the object is dropped from rest, the initial velocity ("vi") is zero. This further simplifies the equations to these:

g = vf /t d = 1/2 gt2 vf2 = 2gd

The sign convention that we will use for direction is this: "down" is the negative direction. If you are given a velocity such as -5.0 m/s, we will assume that the direction of the velocity vector is down. Also if you are told that an object falls with a velocity of 5.0 m/s, you would substitute -5.0 m/s in your equations. The sign convention would also apply to the acceleration due to gravity as shown above. The direction of the acceleration vector is down (-9.81 m/s2) because the gravitational force causing the acceleration is directed downward.

hope this info helps you out!

7 0
3 years ago
A uniformly charged conducting plate with area a has a total charge Q which is positive. The figure below shows a cross-sectiona
givi [52]

Answer:

a)  E = σ / 2 ε₀ =   Q / 2A ε₀, b)  E = 2Q/A ε₀

Explanation:

For this exercise we can use Gauss's Law

        Ф = E. dA = q_{int} / ε₀

Let us define a Gaussian surface as a cylinder with the base parallel to the plane. In this case, the walls of the cylinder and the charged plate have 90 degrees whereby the scalar product is zero, the normal vector at the base of the cylinder and the plate has zero degrees whereby the product is reduced to the algebraic product

              Φ = E dA = q_{int} / ε₀       (1)

 

As they indicate that the plate has an area A, we can use the concept of surface charge density

             σ = Q / A

             Q = σ A

             

The flow is to both sides of loaded plate

            Φ = 2 E A

Let's replace in equation 1

             2E A = σA / ε₀  

             E = σ / 2 ε₀ =   Q / 2A ε₀

This is in the field at point P.

b) Now we have two plates each with a load Q and 3Q respectively and they ask for the field between them

         

The electric field is a vector quantity

         E = E₁ + E₂

In the gap between the plates the two fields point in the same direction whereby they add

         σ₁ = Q / A

         E₁ = σ₁ / 2 ε₀

For the plate 2

         σ₂ = -3Q / A = -3 σ₁

         E₂ = σ₂ / 2 ε₀  

         E₂ = -3 σ₁ / 2 ε₀

The total field is

         E = σ₁ / 2 ε₀  + 3 σ₁ / 2 ε₀  

        E = σ₁ / 2 ε₀  (1+ 3)

        E = 2 σ₁ / ε₀

        E = 2Q/A ε₀  

3 0
3 years ago
Jupiter’s strength of gravity is greater than Earth’s strength of gravity. A person’s will be the same on Jupiter and Earth. A p
stepan [7]
A person's weight will be greater on Jupiter than on earth
8 0
4 years ago
Read 2 more answers
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