A submarine dives to a depth of 100-m beneath the surface of the Pacific Ocean. The density of sea water is 1030 kg/m3. The submarine has a hatch with an area of 2 m2 located on the top of the submarine. No need to show work. a) Calculate the gauge pressure applied on the submarine at the depth of 100 m. b) Calculate the absolute pressure applied on the submarine at the depth of 100 m. Assume the atmospheric pressure in the air above the ocean is one atmosphere. c) Calculate how much force is required in order to open the hatch from the inside of submarine. Assume that the pressure inside the submarine is one atmosphere.

Answer:

the  magnitude of the dipole moment is 3.5*10^-11Cm

Explanation:

The dipole moment is given by the following formula:

[tex]\mu=qr[/tex]

r: distance between the centers of the charges = 500mm

q: charges of the bowling balls = 0.70nC

By replacing you obtain:

[tex]\mu=(0.70*10^{-9}C)(500*10^{-4}m)=3.5*10^{-11}Cm[/tex]

hence, the magnitude of the dipole moment is 3.5*10^-11Cm

Final answer:

The question involves calculating the wavelength and diffraction patterns of electrons in a single slit experiment. The student would use the de Broglie wavelength formula and the principles of single slit diffraction to find the dimensions of the central maximum. It demonstrates the wave-particle duality exhibited by electrons.

Explanation:

The student is seeking to understand how to find the wavelength and diffraction patterns of electrons. The context involves an electron beam passing through a single slit, creating a diffraction pattern on a distant screen. From the given potential difference, one could calculate the de Broglie wavelength of the electrons, as their velocity can be determined under the assumption that they are nonrelativistic. The central maximum's width on the diffraction pattern can be deduced using the slit width and the wavelength.

The phenomenon of diffraction and interference highlighted in the question is a demonstration of the wave-like properties of electrons, referred to as wave-particle duality. The experimental setup often includes narrow slits whose sizes are comparable to the wavelength of electrons, resulting in observable wave effects such as constructive and destructive interference.

The angular positions of the minima and maxima in the diffraction pattern are crucial for determining the dimensions of the pattern. The de Broglie wavelength plays a significant role in these calculations, linking the microscopic quantum world to observable macroscopic patterns.

Answer:No it does not the chemical equation is unbalanced,this is because according to the law of conservation it states that mass cannot be created or destroyed ,the chemical equation N₂ + H₂ → NH₃ shows that energy has been created which is not possibly so the correct balanced chemical is equation is  1N₂ +3H₂ → 3NH₃

Explanation:

The largest mass that block C can have so that blocks A and B still slide together, given the values, is approximately 10.2 kg.

The subject of this question is a physics problem involving static friction, mass, and gravity. The largest mass that block C can have so that blocks A and B still slide together can be calculated using the principle of static friction and the relevant equation:

fs_max = µs (mA + mB)g, with fs_max representing the maximum force of static friction, µs=0.75 being the coefficient of static friction, and g=9.8 m/s² being the acceleration due to gravity. Here mA=8 kg and mB=5 kg are the masses of block A and B respectively.

To keep A and B together, the tension (T) in the string must be less than or equal to fs_max. As T is also equal to the weight (mCg) of block C, from where we can find mC ≤ fs_max / g. Substituting the given values and calculations, we find that the maximum mass of block C should be around 10.2 kg for blocks A and B to slide together.

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Final answer:

The maximum mass that block C can have to prevent sliding between block A and B is calculated using the static friction coefficient [tex](\mu_s)[/tex] and the weight of block B [tex](m_B)[/tex], which results in a mass of 3.75 kg for block C.

Explanation:

To figure out the largest mass that block C can have without block A and B sliding relative to each other, we must use the static friction force and Newton's second law. The static friction force [tex](f_s)[/tex] is what keeps block B from sliding on block A.

This force is given by [tex]f_s = \mu_s \times N[/tex], where μ_s is the coefficient of static friction and N is the normal force. Since block B is at rest on block A, N is equal to the weight of block B, [tex]N = m_B \times g[/tex].

For block A and block B to accelerate together, the tension in the string (T) caused by the weight of block C must not exceed the static friction force. Therefore, the maximum force that can be applied by block C before block B starts sliding is the static friction force: T ≤ f_s.

So, the maximum weight (and hence mass) that block C can have is when [tex]T = f_s[/tex]. Since [tex]T = m_C \times g[/tex] for block C, we have m_C × g = μ_s × m_B × g. Canceling out g and solving for m_C gives us the formula [tex]m_C = \mu_s \times m_B[/tex].

Substituting the given values, we get [tex]m_C = 0.750 \times 5.00 kg = 3.75 kg[/tex]. Hence, the largest mass that block C can have without causing sliding between block A and B is 3.75 kg.

First: CT Scan

Second: Fluoroscopy

Explanation:

Both correct

A CT scan can provide detailed images of a tumor and its surrounding area, which can be beneficial for a cancer patient. For ongoing throat issues, a Barium swallow study can be used, where the patient swallows a barium solution that is then visualized with an X-ray to identify abnormalities.

In the first scenario, the patient with an ongoing history of cancer might benefit most from a Computed Tomography (CT) scan. CT scans are capable of creating detailed pictures of organs, bones, and other tissues, making it an excellent tool for capturing the size and position of a tumor and surrounding blockages in the abdominal area. Furthermore, it can reveal whether the cancer has spread to other parts of the body.

In the second scenario, Joe's doctor chooses to use X-ray imaging to detect any abnormalities in his throat. The specific procedure used for this is known as a Barium swallow study. This involves swallowing a barium solution that coats the esophagus, enabling the X-ray to capture clear images of the region as the patient swallows.

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Answer:

[tex]\Delta s = 0.978\,m[/tex]

Explanation:

The pinball-spring system is modelled after the Principle of Energy Conservation:

[tex]U_{g,1} + U_{k,1} + K_{1} = U_{g,2} + U_{k,2} + K_{2}[/tex]

[tex]-(0.5\,kg)\cdot \left(9.807\,\frac{m}{s^{2}}\right) \cdot \Delta h + \frac{1}{2}\cdot \left(120\,\frac{N}{m}\right)\cdot (-0.2\,m)^{2} = 0[/tex]

The height reached by the pinball is:

[tex]\Delta h = 0.489\,m[/tex]

The distance travelled by the pinball is:

[tex]\Delta s =\frac{0.489\,m}{\sin 30^{\circ}}[/tex]

[tex]\Delta s = 0.978\,m[/tex]

Answer:

volume flow rate:2.68m³/s

diameter :58.27cm

Explanation:

flow rate = Q = πr² v  = amount per second that flows through the pipe

Given:

pipe's diameter= 0.581

r= 0.581/2=>0.2905m

speed 'v'= 10.1 m/s

Q= (3.142)(0.2905)²(10.1)

so

volume flow rate= 2.68m³/s

->if no oil has been added or subtracted or compressed then Q is the same everywhere

therefore,

Q= πr²v

2.68 = π(d/2)²(5.85)

d= (2.68x4) /(3.142 x 5.85)

d= 0.5827m =>58.27cm

Answer:

T

Explanation:

Answer:

true

Explanation:

Answer:

The correct option is C

Explanation:

From the question we are told that

  The initial speed of the rocket is  [tex]v_i = 100 m/s[/tex]

    The speed of the rocket engine sound is [tex]V[/tex]

    The final speed of the rocket is  [tex]v_f = 200 \ m/s[/tex]

The speed of the sound at [tex]v_f[/tex] would still remain V this because the speed of sound wave is constant and is not dependent on the speed of the observer(The mountain ) or the speed of the source (The rocket ).

  A clear example when  lightning strikes you will first see (that is because it travels at  the speed of light which is greater than the speed of sound) but it would take some time before you hear the sound of the   lightning

Here we see that the speed of the lightning(speed of sound) does not affect the speed of the sound it generates  

Answer:Identify

Explanation:

Answer:

b

Explanation:

Answer:

the signs of heat and work are; -Q and -W

Explanation:

The first law of thermodynamics is given by; ΔU = Q − W

where;

ΔU is the change in internal energy of a system,

Q is the net heat transfer (the sum of all heat transfer into and out of the system)

W is the net work done (the sum of all work done on or by the system).

Now, The system in this case is the tire and since the air gets warmer, heat must have left the system. Therefore Q is negative (-Q).

Since work is done by the system, W remains negative.

Thus, the signs of heat and work are; -Q and - W

The impulse delivered to the pinball by the launcher is 1.8 kg•m/s to the east

Let us consider east as positive direction and west as negative direction.

Then, from the question, we get that the initial velocity of the pinball is

2m/s towards the west

or u = - 2 m/s

and the mass of the pinball is m = 150g = 0.15 kg

So, the initial momentum of the pinball is:

[tex]P_i=mu\\\\P_i=0.15\times(-2)\;kgm/s\\\\P_i=-0.3\;kgm/s[/tex]

Now, the final velocity of the pinball after being struck by the rod is 10  m/s towards the east,

or v = 10 m/s

So, the final momentum of the pinball is:

[tex]P_f=mu\\\\P_f=0.15\times(10)\;kgm/s\\\\P_f=1.5\;kgm/s[/tex]

Impulse is defined as the change in momentum, that is,

[tex]I=\Delta P\\\\I=P_f-P_i\\\\I=1.5-(-0.3)\\\\I=1.8\;kgm/s[/tex]

The impulse is 1.8 kgm/s towards the east.

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Final answer:

To maximize the power output of a circuit with a 5V battery and three resistors, the resistors should be placed in parallel because this arrangement supplies more current than a series combination, thereby maximizing power.

Explanation:

To maximize the power output for a circuit with a given voltage source, the resistors should be arranged to draw the highest current possible. For resistors connected in parallel, the total resistance of the circuit decreases, as opposed to when they are in series, where it increases. Since power (P) is calculated using the formula P = V^2 / R, where V is the voltage and R is the resistance, minimizing R will maximize P.

Because a parallel configuration guarantees that each resistor gets the full voltage of the battery, the correct answer is: The student should place all resistors in parallel because the battery supplies more current to a parallel combination than to a series combination. This is because in a parallel circuit, the voltage across each resistor is equal to the voltage of the source, which maximizes the current through each resistor due to Ohm's law (I = V/R), and therefore maximizes the total current in the circuit.

Answer option (a) is thus correct: The student should place all resistors in parallel because the battery supplies more current to a parallel combination than to a series combination.

Answer:

Explanation:

λ

given λ = 700 nm

a) for first maxima, d*sin(θ) =  λ

sin(theta) = λ/d

= 700*10^-9/(0.025*10^-3)

= 0.028

theta θ = sin^-1(0.028)

= 1.60 degrees

b) given R = 1 m,

delta_y = λ*R/d

= 700*10^-9*1/(0.025*10^-3)

= 0.028 m or 2.8 cm

c) for first maxima, d*sin(θ) = λ

sin(θ) = λ/d

= 700*10^-9/(2.5*10^-3)

= 0.00028

theta = sin^-1(0.00028)

= 0.0160 degrees

d) R = 25 mm = 0.025 m

δ_y = λ*R/d

= 700*10^-9*0.025/(2.5*10^-3)

= 7*10^-6 m or 7 micro m

e) No. But the position of maxima and minima will be shifted.

Explanation:

The electrical force between charges is given by :

[tex]F_e=\dfrac{kq_eq_p}{r^2}[/tex]

[tex]q_e\ and\ q_p[/tex] are charge on electron and proton respectively.

[tex]F_e=\dfrac{9\times 10^9\times (1.6\times 10^{-19})^2}{1^2}\\\\F_e=2.3\times 10^{-28}\ N[/tex]

The Gravitational force between masses is given by :

[tex]F_G=\dfrac{Gm_em_p}{r^2}[/tex]

[tex]m_e\ and\ m_p[/tex] are masses of electron and proton respectively.

[tex]F_G=\dfrac{6.67\times 10^{-11}\times 9.1\times 10^{-31}\times 1.67\times 10^{-27}}{1^2}\\\\F_G=1.01\times 10^{-67}[/tex]

Ratio of electrical to the gravitational force is :

[tex]\dfrac{F_e}{F_G}=\dfrac{2.3\times 10^{-28}\ N}{1.01\times 10^{-67}\ N}\\\\\dfrac{F_e}{F_G}=2.27\times 10^{39}[/tex]

Hence, this is the required solution.

Final answer:

To find the magnitude of the electrical force between an electron and proton separated by 1 m, we use Coulomb's Law with given constants. The electrical force is calculated to be approximately 2.30 x 10⁻¹⁰ N.

Explanation:

To calculate the magnitude of the electrical force between an electron and proton separated by 1 meter, we use Coulomb's Law which is given by the formula:

F = k * |q¹ * q²| / r²

Where F is the force in Newtons (N), k is the Coulomb constant (8.98755 x 10⁹ N*m²/C²), q1 and q2 are the charges of the proton and electron respectively, and r is the separation distance in meters. Since both the proton and the electron have an elemental charge of 1.60² x 10⁻¹⁹ C, albeit with opposite signs, their charges can be multiplied to give their product in Coulomb's equation. The separation r is 1 meter.

So the magnitude of the electrical force F is calculated as:

F = (8.98755 x 109 N*m²/C²) * (1.60² x 10⁻¹⁹ C)² / 12m²

F ≈ 2.30 x 10¹⁰ N

[tex]w + h = 28[/tex]

[tex]l \times w \times h = v[/tex]

[tex]v = w \times h \times 24[/tex]

[tex]w = 28 - h[/tex]

[tex]h(28 - h) \times 24 = v[/tex]

[tex]24( - {h}^{2} + 28h) = v[/tex]

Answer:

Check the explanation

Explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

The average distance calculated between a person's ears is 0.2 meters. The interaural time difference (ITD) is maximal when the sound source is directly to the side. For air (vs=338 m/s), Δ[tex]t_{max}[/tex] is 591.72 microseconds, and for seawater (vs= 1534 m/s), it is 130.38 microseconds. These calculations illustrate sound localization and the impact of medium on sound propagation.

Understanding Sound Localization and Interaural Time Difference

When a noise occurs directly to the right of a person, the sound waves reach the right ear before the left ear. We can calculate the maximum interaural time difference ( Δ[tex]t_{max}[/tex]) for sound reaching the ears using the given distance between the ears.

(a) The average distance between a person's ears was estimated as 0.2 meters (20 cm).

(b) To calculate Δ[tex]t_{max}[/tex] with the speed of sound in air (vs = 338 m/s), we can use the formula Δ[tex]t_{max}[/tex] = d / vs, where d is the distance between ears. Substituting the values, we get:

Δ[tex]t_{max}[/tex] = 0.2 m / 338 m/s = 0.0005917159763 seconds, or approximately 591.72 microseconds.

(c) Lastly, for sound traveling in seawater at room temperature where vs = 1534 m/s, we similarly get:

Δ[tex]t_{max}[/tex] = 0.2 m / 1534 m/s = 0.0001303763441 seconds, or approximately 130.38 microseconds.

This demonstrates the role of the medium in sound propagation and how it affects the interaural time difference.

Answer:

a) v = 786.93 m/s

b) v = 122.40 m/s

Explanation:

a) To find the average exhaust speed (v) of the engine we can use the following equation:

[tex] F = \frac{v\Delta m}{\Delta t} [/tex]

Where:

F: is the thrust by the engine = 5.26 N

Δm: is the mass of the fuel = 12.7 g

Δt: is the time of the burning of fuel = 1.90 s

[tex]v = \frac{F*\Delta t}{\Delta m} = \frac{5.26 N*1.90 s}{12.7 \cdot 10^{-3} kg} = 786.93 m/s[/tex]

b) To calculate the final velocity of the rocket we need to find the acceleration.

The acceleration (a) can be calculated as follows:

[tex] a = \frac{F}{m} [/tex]

In the above equation, m is an average between the mass of the engine plus the rocket case mass and the mass of the engine plus the rocket case minus the fuel mass:

[tex]m = \frac{(m_{engine} + m_{rocket}) + (m_{engine} + m_{rocket} - m_{fuel})}{2} = \frac{2*m_{engine} + 2*m_{rocket} - m_{fuel}}{2} = \frac{2*25.0 g + 2*63.0 g - 12.7 g}{2} = 81.65 g[/tex]

Now, the acceleration is:

[tex] a = \frac{5.26 N}{81.65 \cdot 10^{-3} kg} = 64.42 m*s^{-2} [/tex]

Finally, the final velocity of the rocket can be calculated using the following kinematic equation:

[tex]v_{f} = v_{0} + at = 0 + 64.42 m*s^{-2}*1.90 s = 122.40 m/s[/tex]

I hope it helps you!

Final answer:

The average exhaust speed of the engine is calculated to be approximately 786.929 m/s, and the magnitude of the final velocity of the rocket if fired in outer space is roughly 94.916 m/s.

Explanation:

To calculate the average exhaust speed (v_ex), we can use the impulse-momentum theorem, which states that impulse is equal to the change in momentum of the system. Impulse is given by the product of the average force exerted by the engine (thrust) and the time interval during which the thrust is applied. If all the fuel is consumed, the change in mass (Δm) is the mass of the fuel.

Impulse = Thrust × Time = 5.26 N × 1.90 s = 9.994 N·s

The momentum change is equal to the mass of the fuel expelled times the average exhaust speed.

Δ(momentum) = Δm × v_ex

Substituting the impulse and solving for v_ex, we get:

v_ex = Impulse / Δm

v_ex = 9.994 N·s / 0.0127 kg = 786.929 m/s

Part B: Final Velocity of the Rocket in Space

The final velocity (V_final) of the rocket in space can be determined using the rocket equation, also known as Tsiolkovsky's rocket equation:

V_final = v_ex × ln(m_initial / m_final)

Where:

Calculating the final velocity:

V_final = 786.929 m/s × ln(0.088 kg / 0.0753 kg) ≈ 94.916 m/s

Answer:

Magnitude of magnetic field is 1.5 x 10^(-8) T in the positive y-direction

Explanation:

From maxwell's equations;

B = E/v

Where;

B is maximum magnitude of magnetic field

E is maximum electric field

v is speed of light which has a constant value of 3 x 10^(8) m/s

We are given, E = 4.5 V/m

Thus; B = 4.5/(3 x 10^(8))

B = 1.5 x 10^(-8) T

Now, for Electric field, vector E to be in the positive x-direction, the product of vector E and vector B will have to be in the positive z-direction when vector B is in the positive y-direction

Thus,

Magnitude of magnetic field is 1.5 x 10^(-8) T in the positive y-direction

Magnitude of magnetic field in the space at given instant in time is [tex]\bold { 1.5 x 10^{-8}\ T}[/tex]  in the positive y-direction.

From Maxwell's equations,

[tex]\bold {B = \dfrac Ev}[/tex]

Where;

B - maximum magnitude of magnetic field = ?

E- maximum electric field  = 4.5 V/m

v- speed of light =  3 x 10^(8) m/s

Put the values in the formula,

[tex]\bold {B = \dfrac {4.5}{3 x 10^8}}\\\\\bold {B = 1.5 x 10^{-8}\ T}[/tex]

When Electric field, is in the positive x-direction, vector B is in the positive y-direction and  the product of vector E and vector B will have to be in the positive z-direction.

Therefore, magnitude of magnetic field in the space at given instant in time is [tex]\bold { 1.5 x 10^{-8}\ T}[/tex]  in the positive y-direction.

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Answer:

0.0549 m

Explanation:

Given that

equation y(x,t)=Acos(kx−ωt)

speed  v = 8.5 m/s

amplitude A = 5.5*10^−2 m

wavelength λ   = 0.5 m

transverse displacement = ?

v = angular frequency / wave number

and

wave number = 2π/ λ

wave number =  2 * 3.142 / 0.5

wave number = 12.568

angular frequency = v k

angular frequency = 8.5 * 12.568

angular frequency = 106.828 rad/sec ~= 107 rad/sec

so

equation y(x,t)=Acos(kx−ωt)

y(x,t)= 5.5*10^−2 cos(12.568 x−107t)

when x =0 and and t = 0

maximum y(x,t)= 5.5*10^−2 cos(12.568 (0) − 107 (0))

maximum y(x,t)= 5.5*10^−2  m

and when x =  x = 1.52 m and t = 0.150 s

y(x,t)= 5.5*10^−2 cos(12.568 (1.52) −107(0.150) )

y(x,t)= 5.5*10^−2 × (0.9986)

y(x,t) = 0.0549 m

so the transverse displacement is  0.0549 m

Answer:

Explanation:

Given a particle of mass

M = 1.7 × 10^-3 kg

Given a potential as a function of x

U(x) = -17 J Cos[x/0.35 m]

U(x) = -17 Cos(x/0.35)

Angular frequency at x = 0

Let find the force at x = 0

F = dU/dx

F = -17 × -Sin(x/0.35) / 0.35

F = 48.57 Sin(x/0.35)

At x = 0

Sin(0) =0

Then,

F = 0 N

So, from hooke's law

F = -kx

Then,

0 = -kx

This shows that k = 0

Then, angular frequency can be calculated using

ω = √(k/m)

So, since k = 0 at x = 0

Then,

ω = √0/m

ω = √0

ω = 0 rad/s

So, the angular frequency is 0 rad/s

Answer:

It is somewhere in between

Explanation:

Wave length of sound from each of the  speakers = 340 / 1700 = 0.2 m = 20 cm

Distance between first speaker and the given point = 4 m.

Distance between second speaker and the given sound

D = √(4² + 2²)

D = √(16 + 4)

D = √20

D = 4.472 m

Path difference = 4.472 - 4 =

0.4722 m.

Path difference / wave length = 0.4772 / 0.2 = 2.386

This is a fractional integer which is neither an odd nor an  even multiple of half wavelength. Hence this point is of neither a perfect constructive nor a perfect destructive interference.

Answer:

a .

15.68

m/s

(b).  

21.72

m

Explanation:

To determine if the arrow will hit the target, we can analyze the projectile motion. By calculating the time of flight and horizontal displacement, we can determine if the arrow will hit the target. The velocity and direction of the arrow at impact can also be determined using the horizontal and vertical components of velocity.

To determine if the arrow will hit the target, we need to analyze the projectile motion of the arrow. First, we need to calculate the time of flight using the equation t = 2 * (v * sin(theta))/g, where v is the initial velocity of the arrow and theta is the launch angle. Next, we can calculate the horizontal displacement using the equation x = v * cos(theta) * t, where x is the distance traveled horizontally. Comparing the calculated horizontal displacement with the distance to the target, we can determine if the arrow will hit the target.

Given the initial velocity of the arrow (230 km/hr), launch angle (3.5 degrees), and distance to the target (50 m), we can convert the initial velocity to m/s (230 km/hr * (1000 m/km) * (1 hr/3600 s)) and use the formulas to calculate time of flight and horizontal displacement. If the horizontal displacement is less than or equal to the distance to the target, the arrow will hit the target.

To find the velocity and direction of the arrow at impact, we can use the equations v_x = v * cos(theta) and v_y = v * sin(theta), where v_x is the horizontal component of velocity and v_y is the vertical component of velocity. Since the angle of impact is not specified, the direction of the arrow at impact will depend on the particular situation.

Answer:

an orange fringe at 0°, yellow fringes at ±50° and red fringes farther out.

Explanation:

In the visible spectrum- red to violet, red has the highest wavelength.

The maximum internsity  for diffraction grating is given by,

Sinθ[tex](_{max} )[/tex] = mλ/d

It is concluded that the angle of diffraction increases with increase in wavelength'λ' .  So, red fringe will be farthest from the center, orange light will be at the center and yellow fringe will be at 50°.

Therefore, The new pattern consists of : an orange fringe at 0°, yellow fringes at ±50° and red fringes farther out.

Answer:

Check the explanation

Explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

The energy an object has as a result of motion is known as kinetic energy.A force must be applied to an object in order to accelerate it.We must put in effort in order to apply a force.After the work is finished, energy is transferred to the item, which then moves at a new, constant speed.

Solve the problem ?

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Final answer:

To determine the maximum distance the stone can slide on a rough surface, divide the kinetic energy by the friction force. The maximum distance is 48 meters.

Explanation:

To determine the maximum distance the stone can slide on a rough surface, we need to calculate the work done by the friction force.

Work done = Force x Distance

Given that the friction force is 0.50 N and the stone has 24 J of kinetic energy, we can rearrange the equation to solve for distance:

Distance = Kinetic energy / Friction force

Plugging in the values, we get:

Distance = 24 J / 0.50 N = 48 meters

Therefore, the maximum distance the stone can slide on the rough surface is 48 meters.

Answer:

Explanation:

This is a problem based on interference pf light waves.

wavelength of light λ = 553 nm

slit separation d = .134 x 10⁻³ m

screen distance D = 4.5 m

for fourth order bright fringe, path- length  difference = 4 x λ

= 4 x 553

= 2212 nm .

= 2.212 μm

Answer:

Explanation:

the angular frequency ω    of the pendulum is given by the formula

ω  = [tex]\sqrt{\frac{k}{m} }[/tex]    , k is spring constant , m is mass attached .

= [tex]\sqrt{\frac{9}{.3} }[/tex]

= 5.48 rad /s

time period = 2π / ω

= 2 x 3.14 / 5.48

= 1.146 s

b )  formula for speed

v = ω[tex]\sqrt{(a^2-\ x^2)}[/tex]    , a is amplitude , x is displacement from equilibrium point.

for maximum speed x = 0

max speed = ωa

= 5.48 x 3.8 x 10⁻²  ( initial displacement becomes amplitude that is 3.8 cm )

= .208 m /s

20.8 cm / s

c )

when x = .02 m , velocity = ?

v = ω[tex]\sqrt{(a^2-\ x^2)}[/tex]  

=  5.48 [tex]\sqrt{(.038^2-\ .02^2)}[/tex]

= 5.48 x .0323109

= .177 m /s

17.7 cm /s .

Answer:

The angle of incidence is  [tex]\theta_i =42.6^o[/tex]

Explanation:

The diagram for this question is shown on the first uploaded image

From the question we are told that

   The distance between the mirror and the wall is  [tex]a = 33.7 cm[/tex]

    The height of the above the mirror is  [tex]b = 36.7 cm[/tex]

Generally the angle which the reflected ray make with the mirror is mathematically evaluated as

             [tex]\alpha =tan ^{-1} (\frac{b}{a})[/tex]

substituting values

             [tex]\alpha = tan ^{-1}( \frac{36.7}{33.7})[/tex]

            [tex]\alpha =47.4^o[/tex]

From the diagram we can deduce that  the angle of incidence is

             [tex]\theta_i = 90 - \alpha[/tex]

So          [tex]\theta_i = 90 - 47.4[/tex]

              [tex]\theta_i =42.6^o[/tex]