A pin fin of uniform, cross-sectional area is fabricated of an aluminum alloy (k= 160 w/m·k). the fin diameter is d= 4.2 mm, and the fin is exposed to convective conditions characterized by h= 231 w/m2·k. it is reported that the fin efficiency is ηf= 0.65. determine (a) the fin length l and the fin effectiveness ɛf. account for tip convection.

Answer:

Explanation:

check the pictures attached to further understand and i hope it works

Answer:

[tex]v = \frac{-384}{5} (1 - \frac{12}{5} e^{ -5t/12})[/tex]

Explanation:

Weight of the firefighter, W = 192 lb

W = mg

g = 32 ft/s²

Mass of the firefighter, m = W/g

m = 192/32

m = 6 slugs

k = 2.5 lb-s/ft

The force, F = ma = kv

2.5v = 6a

a = 2.5v/6

a = 5v/12

The fundamental dynamic equation;

dv/dt + drag + gravity = 0

dv/dt = -g-a

dv/dt = -32-5v/12..............(a)

The motion will attain terminal velocity when dv/dt = 0

-32 - 5v/12 = 0

-32 = 5v/12

-384 = 5v

v₀ = -384/5

v₀ = -384/5

dv/dt = -32 - 5v/12

[tex]\frac{dv}{-32 -5v/12} = dt[/tex]

[tex]-12/5 ln(32 + 5v/12) = t + c\\ln(32 + 5v/12) = -5t/12 + lnc\\ln(32 + 5v/12) - ln c = -5t/12\\ln\frac{32 + 5v/12}{c} = -5t/12[/tex]

Take exponential of both sides

[tex]\frac{32 + 5v/12}{c} =e^{ -5t/12}\\32 + 5v/12 = ce^{ -5t/12}\\5v/12 = -32 + ce^{ -5t/12}\\v = 12/5 (-32 + ce^{ -5t/12})\\[/tex]

c = v₀ = -384/5

[tex]v = 12/5 (-32 - \frac{384}{5} e^{ -5t/12})\\v = \frac{-384}{5} (1 - \frac{12}{5} e^{ -5t/12})[/tex]

Answer:

7.54 x[tex]10^{-7}[/tex] C

Explanation:

The complete question is:

Students in an introductory physics lab are performing an experiment with a parallel-plate capacitor made of two circular aluminum plates, each 19 cm in diameter, separated by 1.0 cm.How much charge can be added to each of the plates before a spark jumps between the two plates? For such flat electrodes, assume that value of 3×106N/C of the field causes a spark.

SOLUTION:

As you know that, parallel plate capacitance can be defined as

C=εo A/d

Where,

εo is the permittivity of free space constant, A is area of the capacitor plates, and d is the distance between them

Also, C= Q/V

where,

'Q' defines charge stored on the capacitor and 'V' express the potential difference between the plates.

Equating the equations.

εo A/d =  Q/V

Q= (εo A V)/d

for a uniform electric field (such as the one between the plates of a parallel-plate capacitor)

V= Ed ->where 'E' defines magnitude of the electric field.

Therefore,

Q= (εo A E d)/d  =>εo A E ->eq(1)

The area of the plates is given by

A= πr² => π(d/2)² =>π(0.19/2)

A=0.0284m²

Given: E= 3 x [tex]10^{6}[/tex] N/C

Substituting all the required values in eq(1)

(1)=> Q= (8.85x[tex]10^{-12}[/tex]) (-.0284)(3 x [tex]10^{6}[/tex] )

Q= 7.54 x[tex]10^{-7}[/tex] C

Therefore,7.54 x[tex]10^{-7}[/tex] C can be added to each of the plates before a spark jumps between the two plates

Answer: C = Q/4πR

Explanation:

Volume(V) of a sphere = 4πr^3

Charge within a small volume 'dV' is given by:

dq = ρ(r)dV

ρ(r) = C/r^2

Volume(V) of a sphere = 4/3(πr^3)

dV/dr = (4/3)×3πr^2

dV = 4πr^2dr

Therefore,

dq = ρ(r)dV ; dq =ρ(r)4πr^2dr

dq = C/r^2[4πr^2dr]

dq = 4Cπdr

FOR TOTAL CHANGE 'Q', we integrate dq

∫dq = ∫4Cπdr at r = R and r = 0

∫4Cπdr = 4Cπr

Q = 4Cπ(R - 0)

Q = 4CπR - 0

Q = 4CπR

C = Q/4πR

The value of C in terms of Q and R is [Q/4πR]

Answer:

The kinetic energy of the merry-go-round is [tex]\bf{475.47~J}[/tex].

Explanation:

Given:

Weight of the merry-go-round, [tex]W_{g} = 826~N[/tex]

Radius of the merry-go-round, [tex]r = 1.17~m[/tex]

the force on the merry-go-round, [tex]F = 57.8~N[/tex]

Acceleration due to gravity, [tex]g= 9.8~m.s^{-2}[/tex]

Time given, [tex]t=3.47~s[/tex]

Mass of the merry-go-round is given by

[tex]m &=& \dfrac{W_{g}}{g}\\~~~~&=& \dfrac{826~N}{9.8~m.s^{-2}}\\~~~~&=& 84.29~Kg[/tex]

Moment of inertial of the merry-go-round is given by

[tex]I &=& \dfrac{1}{2}mr^{2}\\~~~&=& \dfrac{1}{2}(84.29~Kg)(1.17~m)^{2}\\~~~&=& 57.69~Kg.m^{2}[/tex]

Torque on the merry-go-round is given by

[tex]\tau &=& F.r\\~~~&=& (57.8~N)(1.17~m)\\~~~&=& 67.63~N.m[/tex]

The angular acceleration is given by

[tex]\alpha &=& \dfrac{\tau}{I}\\~~~&=& \dfrac{67.63~N.m}{57.69~Kg.m^{2}}\\~~~&=& 1.17~rad.s^{-2}[/tex]

The angular velocity is given by

[tex]\omega &=& \alpha.t\\~~~&=& (1.17~rad.s^{-2})(3.47~s)\\~~~&=& 4.06~rad.s^{-1}[/tex]

The kinetic energy of the merry-go-round is given by

[tex]E &=& \dfrac{1}{2}I\omega^{2}\\~~~&=&\dfrac{1}{2}(57.69~Kg.m^{2})(4.06~rad.s^{-1})^{2}\\~~~&=& 475.47~J[/tex]

Answer (C)

Explanation:HOPE THIS HELPS

The direction of the magnetic field at point Z is into the page.

The magnetic field is the region of space where a charged object experiences magnetic force when it is moving.

When a charged particle such as an electron or proton moves inside a conductor, magnetic lines of force rotate around the particle. Since, this relative motion caused the magnetic field to generate.

A wire runs left to right and carries a current in the direction shown (attached diagram).

A horizontal line representing a wire. There is a vector right labeled I. There is a point labeled Z below the line.

According to the Fleming's right hand rule, the direction of magnetic field is into the page.

Thus, the direction of the magnetic field at point Z is into the page.

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Answer:

Maximum temperature of the water at the bottom of the fall, θ₂ = 16.09°C

Explanation:

The height of the waterfall,  H = 807 m

At the top of the fall, [tex]\theta_{1} = 14.2^{0} C[/tex]

For water, the specific heat capacity, C = 4200 J/kg/°C

Potential energy at the top of the waterfall, PE = mgH

According to the principle of conservation of energy,

Kinetic energy at the bottom of the waterfall = Potential energy at the top

Therefore, KE = mgh

Applying the conservation of energy again,

KE at the bottom = Heat Energy due to raise in temperature

Heat energy due to raise in temperature = MCΔθ

MCΔθ = MgH

CΔθ  = gH                        

Δθ  = gH/C

Δθ  = (9.81*807)/4200

Δθ  = 1.89°C

[tex]\triangle \theta = \theta_{2} - \theta_{1}[/tex]

1.89 = θ₂ - 14.2

θ₂ = 14.2 + 1.89

θ₂ = 16.09°C

Final answer:

The force exerted by the fish on the line is 35.87 N.

Explanation:

The force exerted by the fish on the line can be calculated using the equation:

Torque = Moment of Inertia x Angular Acceleration

In this case, the moment of inertia of the fishing reel can be calculated using the formula:

Moment of Inertia = [tex]0.5 x Mass x Radius^2[/tex]

Substituting the given values, we can calculate the moment of inertia and then solve for the force exerted by the fish:

Moment of Inertia =[tex]0.5 x 0.7 kg x (5.24 cm)^2[/tex]

Angular Acceleration = [tex]65.7 rad/s^2[/tex]

Using the equation Torque = Moment of Inertia x Angular Acceleration, we can rearrange the equation to solve for the force:

Torque = Force x Radius

Solving for the force:

Force = Torque / Radius

Substituting the given values, we can calculate the force exerted by the fish:

Force = 1.88 N.m / (5.24 cm)

Converting the radius to meters:

Force = 1.88 N.m / (0.0524 m) = 35.87 N

The force exerted by the fish on the line is calculated using the reel's moment of inertia, angular acceleration, and the restraining torque applied by the clutch. The resulting force is found to be 37.08 N.

To find the force that the fish exerts on the line, we need to consider the torque and angular acceleration.

I = 0.5 * m * r²

m = 0.7 kg (mass of the reel)

r = 0.0524 m (radius of the reel, converted from cm to meters)

Therefore:

I = 0.5 * 0.7 kg * (0.0524 m)² = 9.62 * 10⁻⁴ kg·m²

α = 65.7 rad/s²

Using Newton's second law for rotation, we find the net torque (τ_net) on the reel:

τ_net = I * α

τ_net = 9.62 * 10⁻⁴ kg·m² * 65.7 rad/s² = 0.0632 N·m

τ_fish = τ_net + τ_friction

τ_fish = 0.0632 N·m + 1.88 N·m = 1.9432 N·m

τ_fish = F * r

F = τ_fish / r

F = 1.9432 N·m / 0.0524 m = 37.08 N

Thus, the force exerted by the fish on the line is 37.08 N.

Complete Question: A cylindrical fishing reel has a mass of 0.7 kg and a radius of 5.24 cm. A friction clutch in the reel exerts a restraining torque of 1.88 N · m if a fish pulls on the line. The fisherman gets a bite, and the reel begins to spin with an angular acceleration of 65.7 rad/s 2 . What force does the fish exert on the line? Answer in units of N.

Answer:

answer is A

Explanation:

Answer:

A.ligaments and tendons

Explanation:

To find the minimum thickness of the film, one should understand thin film interference. For minimum reflection, this corresponds to the condition of destructive interference. Using this knowledge, the minimum thickness can be calculated using the provided values.

One needs to understand thin film interference to solve this problem. This concept involves understanding how light waves interact when they hit a thin film, and this interaction depends on the film's thickness, the light's wavelength, and the medium's indices of refraction.

Given that minimum reflection is obtained for a wavelength of 512 nm, we know that this condition corresponds to destructive interference. For destructive interference in a thin film like the one we're discussing, the additional distance traveled by the second ray of the light (which reflects off the lower surface of the film) must be odd multiples of λ/2, where λ is the wavelength of the light in the medium of the film.

In this case, we know that the film is made of alcohol and the light in this medium has a different wavelength than in vacuum, given by λ' = λ/n. Here, n is the refractive index of alcohol, so λ' = 512 nm/1.36.

For minimum thickness, and therefore first-order destructive interference, we have that 2t = λ'/2, or t = λ'/4, where t is the thickness of the film, the thing we're looking to find. Substituting in our value for λ', we can calculate that the minimum thickness of the film would be 512 nm/(1.36 x 4).

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The minimum thickness of the film is approximately 470.6 nm.

To find the minimum thickness of the film, we need to consider the conditions for constructive and destructive interference for normally incident light on a thin film.

For destructive interference (minimum reflected light), the optical path difference between the reflected rays from the top and bottom surfaces of the film must be an odd multiple of half the wavelength of the light in the medium of the film. This can be expressed as:

[tex]2n_f_t = (2m + 1)\frac{\lambda_d}{2}[/tex]

where [tex]\( n_f \)[/tex] is the refractive index of the film, (t) is the thickness of the film, [tex]\( \lambda_d \)[/tex] is the wavelength of the light in air for which destructive interference occurs, and (m) is an integer.

For constructive interference (maximum reflected light), the optical path difference must be an even multiple of half the wavelength of the light in the medium of the film. This can be expressed as:

[tex]2n_f_t = m\lambda_c[/tex]

where [tex]\( \lambda_c \)[/tex] is the wavelength of the light in air for which constructive interference occurs.

Given that the destructive interference occurs at [tex]\( \lambda_d = 512 \)[/tex] nm and the constructive interference occurs at [tex]\( \lambda_c = 640 \)[/tex] nm, we can set up two equations using the above conditions:

For destructive interference:

[tex]2 \times 1.36 \times t = (2m + 1)\frac{512}{2}[/tex]

For constructive interference:

2 x 1.36 x t = m x 640

We can solve these two equations simultaneously to find the minimum thickness (t). Let's first express (m) in terms of (t) from both equations:

From destructive interference:

2 x 1.36 x t = (2m + 1) x 256

[tex]t = \frac{(2m + 1) \times 256}{2 \times 1.36}[/tex]

From constructive interference:

2 x 1.36 x t = m x 640

[tex]t = \frac{m \times 640}{2 \times 1.36}[/tex]

Since the thickness (t) must be the same for both conditions, we can equate the two expressions for (t):

[tex]\frac{(2m + 1) \times 256}{2 \times 1.36} = \frac{m \times 640}{2 \times 1.36}[/tex]

2m + 1 x 256 = m x 640

512m + 256 = 640m

256 = 640m - 512m

256 = 128m

m = 2

Now that we have the value of (m), we can substitute it back into either equation to find (t). Using the destructive interference equation:

[tex]t = \frac{(2 \times 2 + 1) \times 256}{2 \times 1.36}[/tex]

[tex]t = \frac{5 \times 256}{2.72}[/tex]

[tex]t = \frac{1280}{2.72}[/tex]

t = 470.6 nm

The given diagram of the magnet shows attraction which occurs between opposite poles therefore, A and C could both be the north poles. Thus, the correct option is C.

A magnet is a material or an object which produces a magnetic field around itself. The magnetic field of this magnet is invisible however it is responsible for the most notable property of a magnet which is a force that is responsible for pulling on other ferromagnetic materials, such as iron, steel, nickel, cobalt, etc. towards it and attracts or repels other magnets as well.

Some important properties of magnet include a magnet has two poles which are north pole and south pole, magnets attract ferromagnetic materials, the similar poles of two magnets repel each other, whereas the opposite poles of two magnets attract each other. A magnet hung up in the air always comes to rest facing the north-south direction. The poles of a magnet are arranged in pairs.

Therefore, the correct option is C.

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Answer:

Work done

Explanation:

The work done on an object is given as the product of force and distance traveled by the object.

J = Ft (Ns)

The change in the momentum of an object is equal to the impulse experienced by the object.

The work done on an object is given as the product of force and distance traveled by the object.

W = Fd (J)

The work done on an object causes change in the position of the object.

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Answer:

y = 0.1sin(4.5x - 345.6t)

Explanation:

Parameters given:

Length of 5 wavelengths = 7 m

Length of one wavelength, λ = 7/5 = 1.4 m

Frequency of wave, f = 55 Hz

Peak to Valley displacement = 20 cm = 0.2 m

Amplitude is half of the Peak to Valley displacement = 0.1 m

The wave function of a wave traveling in the positive x direction is given generally as:

y = Asin(kx - wt)

Where A = amplitude

k = Wave factor = 2π/λ

x = displacement on the x axis

w = angular frequency = 2πf

t = time taken

=> Wave factor, k = 2π/λ = 2π/(1.4) = 4.5 m^(-1)

=> Angular frequency, w = 2πf = 2π * 55 = 345.6 Hz

Therefore, inserting all the necessary parameters, we get that the wave function is:

y = 0.1sin(4.5x - 345.6t)

Answer:

A conduction is the answer

Explanation:

Answer: Radiation

Explanation:

Conduction involves thermal energy between a conductor/insulator, convection is when warm fluids rise and cool fluids sink due to a distinction in the density of their particles. None of these match a marshmallow over fire. Radiation is the correct answer.

Answer:

diffracted into semicircular waves. constructive interference occurs where the waves are crest to crest or trough to trough, destructive interference occurs where they are crest to trough. The light that falls on the screen produces bands of light and dark fringes on the screen as a result of these constructive and destructive interferences. This is called the young's slit experiment.

Laser light passing through two closely spaced slits and shining on a screen will produce an interference pattern of bright and dark fringes due to the wave properties of light, specifically diffraction and interference, which is illustrated through Young's double-slit experiment.

When a laser light passes through two closely spaced slits and shines on a screen, it creates an interference pattern known as interference fringes. This phenomenon occurs due to the wave property of light known as diffraction and interference. Light waves passing through the two slits interfere with each other, creating a series of bright and dark lines or fringes on the screen.

The bright lines, called constructive interference, happen when the light waves enhance each other, and the dark lines, called destructive interference, occur when the light waves cancel each other out. The spacing and number of these fringes depend on the wavelength of the laser light and the distance between the slits. This is illustrated through Young's double-slit experiment.

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Answer:

 k = 2.65 10² N / m

Explanation:

As the pellets shoot up we can use energy conservation

Starting point. Compressed spring rifle

            Em₀ = Ke = ½ k x²

Final point. Highest point of the path

            [tex]Em_{f}[/tex] = U = m g y

Energy is conserved

            Em₀ = Em_{f}

           ½ k x² = m g y

           k = 2 m g y / x²

Let's calculate

            k = 2  1.06 10⁻²  9.8  6.26 / (6.61 10⁻²)²

             k = 2.65 10² N / m

Answer:

-4.3 kgm/s

Explanation:

Impulse which the soccer ball experiences is equal to the change in momentum of a body.

It is given mathematically as:

Impulse = m*Δv = [tex]mv - mu[/tex]

Initial momentum of soccer ball = 2 kgm/s

Final momentum of the soccer ball = -2.3 kgm/s

Therefore, Impulse will be:

Impulse = [tex]-2.3 - 2[/tex]

Impulse = [tex]-4.3 kgm/s[/tex]

The impulse put on the soccer ball by the kicker is -4.3 kgm/s.

Answer:

triple covalent bond

Explanation:

A triple covalent bond is formed when three pairs of electrons (six electrons) are shared between the two combining atoms. A triple bond is shown by marking three short lines between the two symbols of the atoms. It requires three more electrons to attain the stable octet.

- Hope this helps! If you need a further explanation please let me know.

Final answer:

A triple covalent bond connects the two nitrogen atoms in this molecule N2.

Explanation:

A triple covalent bond connects the two nitrogen atoms in this molecule. Nitrogen atoms have 5 valence electrons and need to share 3 pairs of electrons to achieve a valence octet. The triple bond between the nitrogen atoms allows them to share 3 pairs of electrons and form a stable diatomic molecule, N2.

Answer:

true

Explanation:

yes because I said so

Answer:

It is always the same as it was before the collision.

Answer:

The answer is C on Edge

Explanation:

Answer:

saturated solution is the correct answer.

Explanation:

Answer:

4.4j

Explanation:

The change in gravitational potential energy of the book is 3.57 J.

The change in gravitational potential energy of the book can be calculated using the equation:

ΔPE = mgh

where ΔPE is the change in potential energy, m is the mass of the book, g is the acceleration due to gravity (9.8 m/s²), and h is the change in height.

In this case, the mass of the book is 1.5 kg, the initial height is 41 cm (or 0.41 m), and the final height is 71 cm (or 0.71 m).

Substituting these values into the equation:

ΔPE = (1.5 kg)(9.8 m/s²)(0.71 m - 0.41 m) = 3.57 J

Therefore, the book's change in gravitational potential energy is 3.57 J.

Answer:

2.36 x 10^5 kg

Explanation:

radius of hose, r = 0.017 m

radius of underground pipe, R = 0.088 m

number of hoses, n = 3

velocity of water in underground pipe, V = 2.7 m/s

Let v is the velocity of water in each hose.

According to the equation of continuity

A x V = n x a x v

π R² x V = n x π x r² x v

0.088 x 0.088 x 2.7 = 3 x 0.017 x 0.017 x v

v = 24.12 m/s

(a) Amount of water poured onto a fire in one hour by all the three hoses              

                    = n x a x v x density of water x time

                    = 3 x 3.14 x 0.017 x 0.017 x 24.12 x 1000 x 3600

                    = 2.36 x 10^5 kg

Thus, the amount of water poured onto the fire in one hour is 2.36 x 10^5 kg.

a) Using the principles of fluid dynamics, specifically the continuity equation, we found that the velocity of water in the hoses is 2.02 m/s. The volume flow rate in the hoses is 0.0055 m³/s. Therefore, the mass of water poured onto a fire in one hour by all three hoses is 19800000 kg.

a) To answer this question, we need to apply the principles of fluid dynamics, specifically the concept of continuity equation which states that the mass flow rate (the mass of water passing through a given spot per unit time) through a pipe system is constant.

First, let's calculate the cross sectional area of the hydrant pipe (A1) which is πr² = π(0.088m)² ≈ 0.0243 m².

Then, calculate the area of one fire hose (A2) which is π(0.017m)² ≈ 0.000907 m².

Since there are three hoses, the total area for the three hoses (A3) is 3 * A2 ≈ 0.00272 m².

Then, we apply the continuity equation, which is

A1v1=A3v3. We can solve for v3 (the velocity of the water in the hoses), v3 = A1v1/A3 ≈ 2.02 m/s.

To find the mass of water delivered in one hour, we first find the volume flow rate in the hoses,

Q= A3v3 = 0.00272 m² * 2.02 m/s ≈ 0.0055 m³/s.

The volume of water in one hour is Q * 3600s = 19800 m³.

Then, since water has a density (ρ) of 1000 kg/m³, the mass (m) of the water is ρ*volume which equals

19800 * 1000 kg = 19800000 kg.

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Answer:

Measurement and Direction

Explanation:

Displacement is a vector quantity because it has magnitude (the measure o displacement)

Answer:

Measurement and direction.

Explanation:

Answer:

The answer to your question is Work = 784.8 Joules

Explanation:

Data

mass = 20 kg

height = 4 m

time = 10 s

Mechanic work is defined as the force applied to a body so it moves a distance.

Formula

    Work = force x distance

Process

1.- Calculate the force

Force = mass x gravity

-Substitution

Force = 20 x 9.81

-Result

Force = 196.2 N

2.- Calculate the Work

Work = 196.2 x 4

-Result

Work = 784.8 Joules

Answer:

Explanation:

We shall apply Newton's laws of cooling .

dT / dt = k ( T₁ - T₂ )

dT is change in temperature in time dt , k is constant , T₁ and T₂ are temperature of cold  object and hot surrounding respectively.

For  the first case of 4 minutes

(14 - 10)/ 4 = k [(14+10) /2 - 38 ]  , T₁ = (14+10) /2 , the average  temperature

1 = - 26 k

Using the formula for next two minutes

T-14 / 2 = k [(14+T) /2 - 38 ]

T-14 / 2 = 1/26[ 38 - (14+T) /2 ]

T / 2 - 7 = 1.46 - .27 - T / 52

T/2 + T/52 = 7 + 1.46 - .27

= .52 T = 8.19

T = 15.75 degree

Answer:

a) 112.5 m

b) 15.81s

Explanation:

a)We can use the following equation of motion to calculate the velocity v of the rocket at s = 500 m at a constant acceleration of a = 2.25 m/s2

[tex]v^2 = 2as[/tex]

[tex]v^2 = 2*2.25*500 = 2250[/tex]

[tex]v = \sqrt{2250} = 47.4 m/s[/tex]

After the engine failure, the rocket is subjected to a constant deceleration of g = -10 m/s2 until it reaches its maximum height where speed is 0. Again if we use the same equation of motion we can calculate the vertical distance h traveled by the rocket after engine failure

[tex]0^2 - v^2 = 2gh[/tex]

[tex]-2250 = 2(-10)h[/tex]

[tex]h = 2250/20 = 112.5 m[/tex]

So the maximum height that the rocket could reach is 112.5 + 500 = 612.5 m

b) Using ground as base 0 reference, we have the following equation of motion in term of time when the rocket loses its engine:

[tex]s + vt + gt^2/2 = 0[/tex]

[tex]500 + 47.4t - 10t^2/2 = 0[/tex]

[tex]5t^2 - 47.4t - 500 = 0[/tex]

[tex]t= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]t= \frac{47.4\pm \sqrt{(-47.4)^2 - 4*(5)*(-500)}}{2*(5)}[/tex]

[tex]t= \frac{47.4\pm110.67}{10}[/tex]

t = 15.81 or t = -6.33

Since t can only be positive we will pick t = 15.81s

Answer:

A) the maximum height this rocket will reach above the launch pad is 614.68 m

B) time elapsed after engine failure before the rocket comes crashing down to the launch pad is 16.025 sec.

Explanation:

Detailed explanation and calculation is shown in the image below

Answer:

D.

Explanation:

development of the space shuttle to allow humans to explore the moon

Answer:

  L = 2.98 m

Explanation:

In this exercise we are told that there is no friction, so we can use energy conservation

Starting point. Compressed spring

        Em₀ = Ke = ½ k x²

Final point. At the highest point of the ramp

        [tex]Em_{f}[/tex] = U = mg h

As there is no friction the energy is conserved

         Emo = Em_{f}

         ½ k x² = mg h

         h = ½ k x² / mg

         h = ½ 400 0.50² / (5.0 9.8)

         h = 1.02 m

This is the height that the body reaches, to calculate the distance traveled on the ramp let's use trigonometry

          sin θ = h / L

         L = h / sin θ

         L = 1.02 / sin 20

         L = 2.98 m