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Answer:

The  angle is  [tex]\theta = 15.48^o[/tex]

Explanation:

From the question we are told that  

     The distance of the dartboard from the dart is  [tex]d = 3.66 \ m[/tex]

     The time taken is  [tex]t = 0.455 \ s[/tex]

The  horizontal component of the speed of the dart is mathematically represented as

      [tex]u_x = ucos \theta[/tex]

where u is the the velocity at dart is lunched

  so

      [tex]distance = velocity \ in \ the\ x-direction * time[/tex]

substituting values

      [tex]3.66 = ucos \theta * (0.455)[/tex]

 =>   [tex]ucos \theta = 8.04 \ m/s[/tex]

From projectile kinematics the time taken by the dart can be mathematically represented as

         [tex]t = \frac{2usin \theta }{g}[/tex]

=>    [tex]usin \theta = \frac{g * t}{2 }[/tex]

       [tex]usin \theta = \frac{9.8 * 0.455}{2 }[/tex]

      [tex]usin \theta = 2.23[/tex]

=>   [tex]tan \theta = \frac{usin\theta }{ucos \theta } = \frac{2.23}{8.04}[/tex]

       [tex]\theta = tan^{-1} [0.277][/tex]

      [tex]\theta = 15.48^o[/tex]

Answer:

5.09 x 10⁵ Nm²/C

Explanation:

The electric flux φ through a planar area is defined as the electric field Ε times the component of the area Α perpendicular to the field. i.e

φ = E A

From the question;

E = (8.0j + 2.0k) ✕ 10³ N/C

r = radius of the circular area = 9.0m

A = area of a circle = π r²           [Take π = 3.142]

A = 3.142 x 9² = 254.502m²

Now, since the area lies in the x-y plane, only the z-component of the electric field is responsible for the electric flux through the circular area.

Therefore;

φ = (2.0) x 10³ x 254.502

φ = 5.09 x 10⁵ Nm²/C

The electric flux is 5.09 x 10⁵ Nm²/C

Answer:

5.81 X 10^3 Ns

Explanation:

Given that

F = At² and F at t = 1.25 s is 781.25 N ?

A = F/t² at t = 1.25 s => F = 781.25/(1.25)² = 500 N/s²

d(Impulse) = Fdt

Impulse = ∫Fdt =∫At²dt evaluated in the interval 2.00 s ≤ t ≤ 3.50 s

Impulse = At³/3 = (500/3)(t³) = 166.7t³ between t = 2.00 s and t = 3.50 s

Impulse = 166.7[3.5³ - 2³] = 166.7[42.875 - 8] = 166.7[34.875] = 5813.7 Ns

5.81 X 10^3 N.s

Answer:

Yes it produces current

Explanation:

Because If this enclosed field is somehow changed, then following the law of electromagnetic induction, a pulse of current will be produced in the loop. Dues to a change is produced in the electric field when the iron parts of a car pass over it, momentarily increasing the strength of the field.

Answer:

Electric field strengh is a measure of the strength of an electric field at a given point in space, equal to the field would induce on a unit electric charge at that point.

Electric field strength is also known as Electric Field Intensity .

Explanation:

Electric Field is also defined as force per charge. The unit will be force unit divided by charge unit. In this case, it will be Newton/Coulomb or N/C.

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Answer:

V2 = 21.44cm^3

Explanation:

Given that: the initial volume of the bubble = 1.3 cm^3

Depth = h = 160m

Where P2 is the atmospheric pressure = Patm

P1 is the pressure at depth 'h'

Density of water = ρ = 10^3kg/m^3

Patm = 1.013×10^5 Pa.

Patm = 101300Pa

g = 9.81m/s^2

P1 = P2+ρgh

P1 = Patm +ρgh

P1 = 1.013×10^5+10^3×9.81×160.

P1 = 101300+1569600

P1 = 1670900 Pa

For an ideal gas law

PV =nRT

P1V1/P2V2 = 1

V2 = ( P1/P2)V1

V2 = (P1/Patm)V1

V2 = ( 1670900 /101300 Pa) × 1.3

V2 = 1670900/101300

V2 = 16.494×1.3

V2 = 21.44cm^3

The volume of the bubble can be determined using ideal gas law. The volume of the bubble when it reaches surface is 21.44 [tex]\bold {cm^3}[/tex].

The formula of the pressure of the static fluid

P1 = P2+ρgh

Where,

P1 -  pressure at depth 'h'

P2 -  atmospheric pressure = [tex]\bold {1.013x10^5 }[/tex] =  1670900 Pa

h - Depth = 160m  

ρ - Density of water = [tex]\bold {10^3\ kg/m^3}[/tex]

g- gravitational acceleration = [tex]\bold {9.81\ m/s^2}[/tex]

The initial volume of the bubble = [tex]\bold {1.3\ cm^3}[/tex]  

[tex]\bold {P1 = 1.013x10^5+10^3\times 9.81\times 160}\\\\\bold {P1 = 101300+1569600}\\\\\bold {P1 = 1670900\ Pa}[/tex]  

 For an ideal gas,  

PV =nRT  

[tex]\bold {\dfrac {P_1V_1}{P_2V_2 }= 1}[/tex]  

[tex]\bold {V2 = \dfrac { P_1}{P_2V_1}}[/tex]

So,

[tex]\bold {V2 = \dfrac {1670900 }{101300 }\times 1.3}\\\\\bold {V2 =21.44\ cm^3}[/tex]  

Therefore, the volume of the bubble when it reaches surface is 21.44 [tex]\bold {cm^3}[/tex].

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Answer:

The mass of the fluid is 72 g.

Explanation:

The following data were obtained from the question:

Height (h) = 10 cm

Area of cross section (A) = 36cm²

Relative density = 0.2

Mass =..?

Next, we shall determine the volume of the cylinder. This can be achieved by doing the following:

Volume = Area x Height

Volume = 36 x 10

Volume = 360 cm³

Next, we shall determine the density of the liquid.

This can be obtained as follow:

Relative density = density of substance/density of water.

Relative density = 0.2

Density of water = 1 g/cm³

Density of fluid =...?

Relative density = density of substance/density of water.

0.2 = density of fluid / 1 g/cm³

Cross multiply

Density of fluid = 0.2 x 1 g/cm³

Density of fluid = 0.2 g/cm³

Finally, we shall determine the mass of fluid as follow:

Volume = 360 cm³

Density of fluid = 0.2 g/cm³

Mass of fluid =...?

Density = mass /volume.

0.2 g/cm³ = mass of fluid /360 cm³

Cross multiply

Mass of fluid = 0.2 g/cm³ x 360 cm³

Mass of fluid = 72 g

Therefore, the mass of the fluid in the jar is 72 g.

Answer:

The speed of the particle is 2.86 m/s

Explanation:

Given;

radius of the circular path, r = 2.0 m

tangential acceleration,  [tex]a_t[/tex] = 4.4 m/s²

total magnitude of the acceleration, a = 6.0 m/s²

Total acceleration is the vector sum of  tangential acceleration and radial acceleration

[tex]a = \sqrt{a_c^2 + a_t^2}\\\\[/tex]

where;

[tex]a_c[/tex] is the radial acceleration

[tex]a = \sqrt{a_c^2 + a_t^2}\\\\a^2 = a_c^2 + a_t^2\\\\a_c^2 = a^2 -a_t^2\\\\a_c = \sqrt{a^2 -a_t^2}\\\\a_c = \sqrt{6.0^2 -4.4^2}\\\\a_c = \sqrt{16.64}\\\\a_c = 4.08 \ m/s^2[/tex]

The radial acceleration relates to speed of particle in the following equations;

[tex]a_c = \frac{v^2}{r}[/tex]

where;

v is the speed of the particle

[tex]v^2 = a_c r\\\\v= \sqrt{a_c r} \\\\v = \sqrt{4.08 *2}\\\\v = 2.86 \ m/s[/tex]

Therefore, the speed of the particle is 2.86 m/s

Answer:

Explanation:

Using the formula for finding the Z score

Z = x-µ/σ

x is the sample size

µ is the sample mean

σ is the standard deviation

For percentage of the resistors will have resistance between 148 Ω and 152 Ω, or is calculated as shown

P(148≤x152) = Z(152-150/5) - Z(148-150/5)

P(148≤x152) = Z(0.4)-Z( - 0.4)

P(148≤x152) = 0.6554-0.3446

The Z values are from the normal distribution table.

P(148≤x152) = 0.3108

The percentage of resistor that will have between 148 and 152 ohms is 0.3108×100% = 31.08%

Similarly for resistances between 140 Ω and 160 Ω

P(140≤x160) = Z(160-150/5) - Z(140-150/5)

P(140≤x160) = Z(2.0)-Z( - 2.0)

P(140≤x160) = 0.9775-0.02275

The Z values are from the normal distribution table.

P(140≤x160) = 0.9547

The percentage of resistor that will have between 140 and 160ohms is 0.9547×100% = 95.47%

The percentage of the resistors will have resistance between 148 Ω and 152 Ω is 31.08%

The percentage of the resistors will have resistance between 140 Ω and 160 Ω is  95.47%

To solve for the probability we will use the standard score of the Z score, which is given by:

Z = (x - µ)/σ

where x is the sample size

µ is the sample mean = 150Ω

σ is the standard deviation = 5Ω

The probability of the resistors with resistance between 148 Ω and 152 Ω, will be:

P(148 ≤ 152) = Z((152-150)/5) - Z((148-150)/5)

P(148 ≤ 152) = Z(0.4)-Z( - 0.4)

P(148 ≤ 152) = 0.6554-0.3446

P(148 ≤ 152) = 0.3108

So, the percentage will be:

0.3108×100% = 31.08%

Similarly for resistances between 140 Ω and 160 Ω

P(140 ≤ 160) = Z((160-150)/5) - Z((140-150)/5)

P(140 ≤ 160) = Z(2.0)-Z( - 2.0)

P(140 ≤ 160) = 0.9775-0.02275

P(140 ≤ 160) = 0.9547

The percentage of resistor that will have between 140 and 160ohms is 0.9547×100% = 95.47%

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Answer:

Explanation:

We shall apply the theory of

heat lost = heat gained .

heat lost by water = mass x specific heat x temperature diff

= .285 x 4190 x ( 75.2 - 32 ) = 51587.28 J  

heat gained by ice to attain temperature of zero

= m x 2100 x 22.8 = 47880 m

heat gained by ice in melting = latent heat x mass

= 334000m

heat gained by water at zero to become warm at 32 degree

= m x 4190 x 32 = 134080 m

Total heat gained = 515960 m

So

515960 m = 51587.28

m = .1 kg

= 100 gm

Answer:

    q = q₀ sin (wt)

Explanation:

In your statement it is not clear the type of circuit you are referring to, there are two possibilities.

1) The circuit of this problem is a system formed by an Ac voltage source and a capacitor, in this case all the voltage of the source is equal to the voltage at the terminals of the capacitor

                    ΔV = Δ[tex]V_{C}[/tex]

we assume that the source has a voltage of the form

                    ΔV = ΔV₀o sin wt

The capacitance of a capacitor is

                   C = q / ΔV

                  q = C ΔV sin wt

the current in the circuit is

                    i = dq / dt

                    i = c ΔV₀ w cos wt

if we use

                  cos wt = sin (wt + π / 2)

we make this change by being a resonant oscillation

we substitute

                  i = w C ΔV₀ sin (wt + π/2)

With this answer we see that the current in capacitor has a phase factor of π/2 with respect to the current

2) Another possible circuit is an LC circuit.

In this case the voltage alternates between the inductor and the capacitor

                     V_{L} + V_{C} = 0

                      L di / dt + q / C = 0

the current is

                      i = dq / dt

they ask us for a solution so that

                    L d²q / dt² + 1 / C q = 0

                     d²q / dt² + 1 / LC q = 0

this is a quadratic differential equation with solution of the form

                    q = A sin (wt + Ф)

to find the constant we derive the proposed solution and enter it into the equation

                di / dt = Aw cos (wt + Ф)

                d²i / dt²= - A w² sin (wt + Ф)

                 - A w² + 1 /LC  A = 0

                  w = √ (1 / LC)

To find the phase factor, for this we use the initial conditions for t = 0

in the case of condensate for t = or the charge is zero

                 0 = A sin Ф

                  Ф = 0

                  q = q₀ sin (wt)

Answer:

Explanation:

Given the formula for calculating the depth in metres expressed as

depth in meters = ½ (1500 m/sec × Echo travel time in seconds)

Given depth of the challenger = 10, 994 meters, we will substitute this given value into the formula given to calculate the time take for the echo to travel.

10, 994 = depth in meters = ½ * 1500 m/sec × Echo travel time in seconds

10,994 = 750 * Echo travel time in seconds

Dividing both sides by 750;

Echo travel time in seconds = 10,994 /750

Echo travel time in seconds ≈ 14.66secs (to two decimal places)

Therefore, it would take an echo sounder’s ping 14.66secs to make the trip from a ship to the Challenger Deep and back

Answer:

destructive interference

Explanation:

As we know that , when the phase difference between the path of two wavelength is 180°, then its known as destructive interference . And when the phase difference between the path of two wavelength is 0°, then its known as constructive interference.

In the constructive interference , the resulting amplitude will be maximum while in the destructive interference , the resulting amplitude will be zero(minimum).

Therefore the answer will be destructive interference.

Answer:

The time interval is [tex]t = 5.48 *10^{-3} \ s[/tex]

Explanation:

From the question we are told that

   The length of the string is  [tex]l = 3.00 \ m[/tex]

    The  mass of the string is [tex]m = 5.00 \ g = 5.0 *10^{-3}\ kg[/tex]

     The  tension on the string is  [tex]T = 500 \ N[/tex]

The  velocity of the pulse is mathematically represented as

      [tex]v = \sqrt{ \frac{T}{\mu } }[/tex]

Where [tex]\mu[/tex] is the linear density which is mathematically evaluated as

       [tex]\mu = \frac{m}{l}[/tex]

substituting values

     [tex]\mu = \frac{5.0 *10^{-3}}{3}[/tex]

     [tex]\mu = 1.67 *10^{-3} \ kg /m[/tex]

Thus  

     [tex]v = \sqrt{\frac{500}{1.67 *10^{-3}} }[/tex]

    [tex]v = 547.7 m/s[/tex]

The time taken is evaluated as

    [tex]t = \frac{d}{v}[/tex]

substituting values

      [tex]t = \frac{3}{547.7}[/tex]

      [tex]t = 5.48 *10^{-3} \ s[/tex]

Explanation:

Answer:

D. The acceleration vector of the plant points towards the center of the circle. (Works for Apex)

Explanation:

Velocity is always changing because to have velocity you require direction and the direction is always changing when orbiting therefore A and C are not true. And B is not true because the speed of the planet is not accelerating when orbiting around a star.

Answer:

C) 200 m/s

Explanation:

The sound travels a total distance of 360 m in 0.03 minutes.

v = (360 m) / (0.03 min × 60 s/min)

v = 200 m/s

Answer:

To reverse the direction of an electric current, we simply reverse the voltage either automatically with the help of some switching circuitry or manually by changing the voltage source terminals connection.  

Explanation:

For electric current to flow, there must be a potential difference, usually referred to as the voltage. The electric current flow is analogous to the flow of water under the action of a pump, through a series of pipe connections. The voltage is similar to the driving action of the pump, and current flows the same way water flows. The resistance due to drag on the pipe wall is equivalent to electric resistance. For current to flow in the reverse direction, the voltage or rather, the potential difference is changed, causing the current to flow in the opposite direction. This can be done by switching the terminals of the voltage source, or by automatic means. The automatic switching can be done with a transistor based circuitry.

Answer:

Peak current= 84.86 A

Area of each turn = 0.029 m^2

Explanation:

The peak value of current can be obtained from Irms= 0.707Io. Where Io is the peak current.

Hence;

Irms= 60.0A

Io= Irms/0.707

Io = 60.0/0.707

Io= 84.86 A

Vrms= 0.707Vo

Vo= Vrms/0.707= 170/0.707 = 240.45 V

From;

V0 = NABω

Where;

Vo= peak voltage

N= number of turns

B= magnetic field

A= area of each coil

ω= angular velocity

But ω= 2πf = 2×π×95= 596.9 rads-1

Substituting values;

A= Vo/NBω

A= 240.45/550×0.025×596.9

A= 0.029 m^2

Answer:

e is correct

Explanation:

When a ball is pushed below the surface of a pool, it is submerged when the buoyant force is approximately equal to the water's weight of the volume that could fill the ball. When the ball is released, the buoyant force becomes greater than the gravitational force so that the ball accelerates upward.

The buoyant force can be described as the upward force exerted on an object wholly or partially immersed in a fluid and is also called Upthrust. A body submerged partially or fully in a fluid due to the buoyant force appears to lose its weight.

The following factors affect buoyant force the density of the fluid, the volume of the fluid displaced, and the local acceleration due to gravity.

When an object immerses in water, the object experiences a force from the downward direction opposite to the gravitational pull, which causes a decrease in its weight. The difference in this pressure gives the upward force on the object, as buoyancy.

Therefore, options (d), (e) are correct.

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Answer:

Heat transfer is the transmission of heat energy from a body at higher temperature to lower temperature. The three mechanisms of heat transfer are

Example of Conduction:

Heating a metal

Example of Convection:

Sea Breeze

Example of Radiation:

Sun

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Answer:

Transmission of heat is the movement of thermal energy from one thing to another thing of different temperature.

There are three(3) different ways heat can transfer and they are:

a) Conduction (through direct contact).

b) Convection (through fluid movement).

c) Radiation (through electromagnetic waves).

Examples: 1.Heating a saucepan of water using a coalpot.(conduction&convection).

2. Baking a pie in an oven(radiation).

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Answer:

The mutual inductance is  [tex]M = 0.000406 \ H[/tex]

Explanation:

From the question we  are told that

    The  number of turns per unit length  is  [tex]N = 1800[/tex]

    The radius is  [tex]r = 0.0165 \ m[/tex]

     The  number of turns of the solenoid is  [tex]N_s = 210 \ turns[/tex]

Generally the mutual inductance of the  system is mathematically represented as

       [tex]M = \mu_o * N * N_s * A[/tex]

Where A is the cross-sectional area of the system which is mathematically represented as

       [tex]A = \pi * r^2[/tex]

substituting values

      [tex]A = 3.142 * (0.0165)^2[/tex]

       [tex]A = 0.0008554 \ m^2[/tex]

also   [tex]\mu_o[/tex] is the permeability of free space with the value  [tex]\mu_o = 4\pi * 10^{-7} N/A^2[/tex]

So  

      [tex]M = 4\pi * 10^{-7} *1800 * 210 * 0.0008554[/tex]

      [tex]M = 0.000406 \ H[/tex]

Answer:

At 3.86K

Explanation:

The following data are obtained from a straight line graph of C/T plotted against T2, where C is the measured heat capacity and T is the temperature:

gradient = 0.0469 mJ mol−1 K−4 vertical intercept = 0.7 mJ mol−1 K−2

Since the graph of C/T against T2 is a straight line, the are related by the straight line equation: C /T =γ+AT². Multiplying by T, we get C =γT +AT³ The electronic contribution is linear in T, so it would be given by the first term: Ce =γT. The lattice (phonon) contribution is proportional to T³, so it would be the second term: Cph =AT³. When they become equal, we can solve these 2 equations for T. This gives: T = √γ A .

We can find γ and A from the graph. Returning to the straight line equation C /T =γ+AT². we can see that γ would be the vertical intercept, and A would be the gradient. These 2 values are given. Substituting, we f ind: T =

√0.7/ 0.0469 = 3.86K.

Answer:

122°C

Explanation:

From the data Final temperature is 0 deg C since there is 0.9kg of ice and 1.10kg of liquid water.

That means that 1.10kg of the ice undergoes Heat of Fusion which is 3.34x10^5 J/kg...

Heat lost by copper = Heat gained by ice + Heat of fusion

-> (7.0kg)(390J/kg*C)(0-T) = (2.00kg)(2100J/kg*C)(0 - (-20) + (1.10kg)(3.34x10^5 J/kg)

-> T(2730) = 334001

-> T = 122°C

Answer:

a) 1764.71 ohms

b) 1.73 H

Explanation:

From the question, we can identify the following parameters;

Vo =12 V , i = 4.86 mA, t =0.700 ms, io =6.80 mA

(a) Indcued emf V = L di/dt =0

From ohms law Vo = ioR

R = 12/6.80*0.001

R=1764.71 ohms

(b) For LR circuit

i =io (1-e^-t/T)

Time constant T = L/R

4.86 = 6.80 (1-e^-0.7*10^-3/T)

divide both side by 6.8

0.715 = 0.0007/T

L/R = 0.0007/0.715

L/R = 0.000979020979

Substitute R from above

L = 0.000979020979 * 1764.71

L =1.73 H

Answer:

Each of the capacitor carries the same charge, Q

Explanation:

When capacitors are connected in series, the battery voltage is divided equally across the capacitors. The total voltage across the three identical capacitors is calculated as follows;

[tex]V_T = V_1 + V_2 + V_3[/tex]

We can also calculate this voltage in terms of capacitance and charge;

[tex]V = \frac{Q}{C} \\\\V_T = V_1 + V_2 +V_3 \\\\(given \ total \ charge \ as \ Q, then \ the \ total \ voltage \ V_T \ can \ be \ written \ as)\\\\V_T = \frac{Q}{C_1} + \frac{Q}{C_2} + \frac{Q}{C_3} \\\\V_T = Q(\frac{1}{C_1 } +\frac{1}{C_2} + \frac{1}{C_3 })\\\\[/tex]

Therefore, each of the capacitor carries the same charge, Q

Answer:

God is omnipresent.

Explanation:

This means God is everywhere and He works where ever we are in the world

Answer:

a= 4.9m/s²

Explanation:

Using Fnet= mgsintheta = ma

But a= gsintheta

a= 9.8xsin 30

= 4.9m/s²

Answer:

the correct answer is c     v₁> 12.5 m / s

Explanation:

This is a one-dimensional kinematics exercise, let's start by finding the link to get up to speed.

            v² = v₀² + 2 a₁ x

as part of rest v₀ = 0

           a₁ = v² / 2x

           a₁ = 25² / (2 120)

           a₁ = 2.6 m / s²

now we can find the velocity for the distance x₂ = 60 m

           v₁² = 0 + 2 a1 x₂

           v₁ = Ra (2 2,6 60)

           v₁ = 17.7 m / s

these the speed at 60 m

we see that the correct answer is c     v₁> 12.5 m / s

Complete Question

One arm of a U-shaped tube (open at both ends) contains water, and the other alcohol.

If the two fluids meet at exactly the bottom of the U, and the alcohol is at a height of 18 cm, at what height will the water be?Assume the density of alcohol is [tex]\rho_a = 790\ kg/m^3[/tex]

Answer:

The  height of water is  [tex]h_w = 0.142 \ m[/tex]

Explanation:

From the question we are told that

    The height of the alcohol is  [tex]h_a =18 \ cm = 0.18 \ m[/tex]

     The  density of the alcohol is  [tex]\rho_a = 790\ kg/m^3[/tex]

Generally the pressure on both arm of the tube are equal given that they are both open

i,e    [tex]P_a = P_w[/tex]

Where  [tex]P_a[/tex] is pressure of alcohol and  [tex]P_w[/tex] is pressure of water

   So the pressure on the arm of the tube containing the alcohol is mathematically evaluated as

         [tex]P_a = g * h * \rho[/tex]

substituting values

         [tex]P_a =9.8 * 0.18 * 790[/tex]

         [tex]P_a = 1394 \ Pa[/tex]

Generally the pressure on the arm of the tube containing the water is mathematically evaluated as

       [tex]P_w = g * h_w * \rho_w[/tex]

where  [tex]\rho_w[/tex] is the density of water which has  a value [tex]\rho _w = 1000 \ kg/m^3[/tex]

So  

      [tex]1394 = 9.8 * h_w * 1000[/tex]

=>    [tex]h_w = \frac{1394}{9800}[/tex]

=>  [tex]h_w = 0.142 \ m[/tex]