1 ) The speed of the roller coaster = 12.28 m / s
2 ) Height of the hill above the top of the loop = 7 m
3 ) Energy lost due to friction = 132 KJ
1 ) The speed of the roller coaster,
[tex]a_{c}[/tex] = v² / r
[tex]a_{c}[/tex] = Centripetal acceleration
v = Linear velocity
r = Radius
r = 14 m
[tex]a_{c}[/tex] = 1.1 g = 1.1 * 9.8
[tex]a_{c}[/tex] = 10.78 m / s²
v² = [tex]a_{c}[/tex] * r
v² = 10.78 * 14
v² = 150.9
v = 12.28 m / s
2 ) Initial starting point,
Considering hill as 1 and the loop as 2,
v1 = 0
h2 = 2 r = 2 * 14
h2 = 28 m
∑ [tex]F_{y}[/tex] = m [tex]a_{c}[/tex]
[tex]F_{N}[/tex] + [tex]F_{g}[/tex] = m [tex]a_{c}[/tex]
0 + m g = m v2² / r
v2² = g r
According to law of conservation of energy,
E1 = E2
m g h1 + 1 / 2 m v1² = m g h2 + 1 / 2 m v2²
m g h1 + 0 = 28 m g + 1 / 2 m g r
h1 = 28 + 1 / 2 ( 14 )
h1 = 35 m
Height of the hill above the top of the loop = h1 - h2
Height of the hill above the top of the loop = 35 - 28
Height of the hill above the top of the loop = 7 m
3 ) Energy lost due to friction,
h1 = 35 + 7.5
h1 = 42.5 m
m = 1800 kg
v2² = g r
v2² = 9.8 * 14
v2² = 137.2 m / s
Since energy is lost due to friction,
KE1 + U1 = KE2 + U2 + W
0 + m g h1 = 1 / 2 m v2² + m g h2 + W
( 1800 * 9.8 * 42.5 ) = ( 0.5 * 1800 * 137.5 ) + ( 1800 * 9.8 * 28 ) + W
749700 = 123750 + 493920 + W
W = 749700 - 617670
W = 132030 J
W = 132 KJ
Therefore,
1 ) The speed of the roller coaster = 12.28 m / s
2 ) Height of the hill above the top of the loop = 7 m
3 ) Energy lost due to friction = 132 KJ
To know more about radius of curvature
https://brainly.com/question/13707458
#SPJ1
The inductor in the RLC tuning circuit of an AM radio has a value of 9 mH. What should be the value of the variable capacitor, in picofarads, in the circuit to tune the radio to 66 kHz
Given:
The inductance is,
[tex]\begin{gathered} L=9\text{ mH} \\ =9\times10^{-3}\text{ H} \end{gathered}[/tex]The radio frequency is,
[tex]\begin{gathered} f=66\text{ kHz} \\ =66\times10^3\text{ Hz} \end{gathered}[/tex]To find:
value of the variable capacitor, in picofarads
Explanation:
The frequency of the AM is,
[tex]\begin{gathered} f=\frac{1}{2\pi\sqrt{LC}} \\ \end{gathered}[/tex]Substituting the values we get,
[tex]\begin{gathered} 66\times10^3=\frac{1}{2\pi\sqrt{9\times10^{-3}\times C}} \\ \sqrt{9\times10^{-3}\times C}=\frac{1}{2\pi\times66\times10^3} \\ \sqrt{9\times10^{-3}\times C}=2.41\times10^{-6} \\ 9\times10^{-3}\times C=5.81\times10^{-12} \\ C=6.45\times10^{-10} \\ C=645\times10^{-12}\text{ F} \\ C=645\text{ pF} \end{gathered}[/tex]Hence, the capacitance is 645 pF.
If Hubble's constant had a value of 95 km/s/Mpc, what would be the age of the Universe?
The age of universe will be 0.0103 million years.
Hubble's law states that the rate at which any galaxy is receding from another galaxy is proportional to its distance from the galaxy. In simple form,
v = H₀ × d
where v is the velocity of the galaxy, d is its distance, and H₀ is the Hubble's constant.
Given: Hubble's constant, H₀ = 95 km/s/Mpc.
The term 1 / H₀ is called the Hubble's time and gives the age of the universe. That is, if 't' is the age of the universe, then
t = 1 / H₀.
Substitute the given value.
⇒ t = 1 / (95 km/s/Mpc)
(1 pc = 3.086 ×[tex]10^{13}[/tex] km)
⇒ t = 1 / (95/3.086 ×[tex]10^{13}[/tex] ) s
⇒ t = (1 / 30.784) ×[tex]10^{13}[/tex] s
⇒ t = 0.0325 ×[tex]10^{13}[/tex] s
(1 year = 3.154 ×[tex]10^{7}[/tex] s)
⇒ t = 10305.68 years
⇒ t = 0.0103 million years
Therefore, the age of universe will be 0.0103 million years.
Learn more about Hubble's law here, https://brainly.com/question/13705068.
#SPJ1
Energy transformations always produce a wasteful amount of energy called ?
Energy transformation always produce a wasteful amount of energy called heat energy.
Hence, the answer is heat energy.
The safe loadof a wooden beam supported at both ends varies jointly as the width, w, the square of the depthd, and inversely as the length A wooden beam 7 inwide, 10 indeepand 19 ft long holds up 4422 What load would a beam inwide. 5 indeep and long of the same material support? (Round off your answer to the nearest pound )
L = k(wd^2/ l)
L = load
L1= 4422 lb
w = width
w1= 7 in
d = depth
d1= 10 in
l = lenght
l1= 19 ft
L2=
w2= 5in
d2=5in
l2= 11ft
First solve the constant with values 1
L1= k [(w1) (d1)^2 / l1]
4422= k [(7) (10)^2 / 19]
k = 4422 / [(7) (10)^2 / 19]
k= 120 lb/ft in^3
Replace with values 2
L2= k [(w2) (d2)^2 / l2]
L2= 120 [(5) (5)^2 / 11]
L2= 1363.63 LB
A dentist causes the bit of a high speed drill to accelerate from an angular speed of 1.76 x 10^4 rads to an angular speed of 4.61 x 10^4 rat. In the process, the bit turns through 1.97 x 10 ^4 rad. Assuming a constant angular acceleration, how long would it take the reach its maximum speed of 7.99 x 10^4 rads starting from rest?
The time taken for the bit to reach the maximum speed is 1.35 seconds.
What is the angular acceleration of the bit?The angular acceleration of the bit is determined by applying the following kinematic equation as shown below.
ωf² = ωi² + 2αθ
where;
ωf is the final angular speedωi is the initial angular speedθ is the angular displacementα is the angular accelerationα = (ωf² - ωi²)/2θ
α = (46,100² - 17,600²) / (2 x 19,700)
α = 46,077.4 rad/s²
The time taken for the bit to reach the maximum speed is calculated as follows;
ωf = ωi + αt
t = (ωf - ωi) / α
t = (79,900 - 17,600) / (46,077.4)
t = 1.35 seconds
Learn more about angular acceleration here: https://brainly.com/question/25129606
#SPJ1
The role or purpose of the battery in a circuit is to ____. Choose three.Group of answer choicesa) supply electric charge so that a current can existb) supply energy to the chargec) move the charge from the - to the + terminal of the batteryd) transform energy from electrical energy into light energye) establish an electric potential difference between the + and - terminalsf) replenish the charge which is lost in the light bulbg) offer resistance to the flow of charge so that the light bulb can get hot
Given:
The battery is connected to a circuit.
To find:
The purpose of the battery in the circuit
Explanation:
A battery is a source of energy in a circuit. The battery provides a push or a voltage to get the current flowing in a circuit.
Hence, the purposes are
b) supply energy to the charge
e) establish an electric potential difference between the + and - terminals
f) replenish the charge which is lost in the light bulb
which of the following are independent of the mass of an object falling freely near earth's surface: (may have more than 1 answer) 1) acceleration of the object 2) gravitational force acting on the object 3) gravitational force acting on the object 4) magnitude of the gravitational field
As the object is falling freely, the acceleration of the object will be equal to the acceleration due to gravity.
It is given as,
[tex]g=\frac{GM}{R^2}[/tex]Here, G is the univarshal gravitational constant and M is the mass of the Earth.
means acceleration of the object is constant and independent of the mass of the object.
so option 1 is correct.
now the gravitational force on that object is,
[tex]F=\frac{GMm}{R^2}[/tex]here this is dependent on the mass of the object(m).
NOw the gravitational field means the force per unit mass and is given by,
[tex]E=\frac{GM}{R^2}[/tex]Here we can se that this gravitational field is also independent of the mass of the object.
So, option 1 and 4 are correct.
Example of a balanced force
A/An _____ is described as a device that is used to measure potential difference across any part of a circuit.ammeterfuseground fault interruptervoltmeter
Answer:
[tex]\text{Voltmeter}[/tex]Explanation: We need to find an instrument that measures potential difference across any part of the circuit, a potential difference is basically voltage difference across a circuit difference and the device used to measure this difference is known as:
[tex]\text{ Voltmeter}[/tex]Voltmeter used in a circuit
A card is drawn at random from a standard deck. Determine whether the events are mutually exclusive or not mutually exclusive. Then find each probability (2 or black card).
Consider that the event are no mutually exclusive because you can obtain a black card and 2 in one card.
In a standard deck you have 52 cards. There are 26 black cards and 4 cards with number 2.
Consider that in the 26 black cards there are two black cards with number 2.
Then, to get the probability consider that the required result can be obtained for 26 + 2 = 28 cards (26 black cards and two cards with number 2).
The probability is the quotient between the number of options over the number of cards:
[tex]p=\frac{28}{52}=0.54[/tex]Hence, the probability is 0.54
A mass of 0.520 kilograms is attached to a spring and lowered into a resting position, causing the spring to stretch 18.7 centimeters. The mass is then lifted up and released. a. What is the spring constant of the spring? Include units in your answer.b. What is the frequency of its oscillation? Include units in your answer.Answer must be in 3 significant digits.
Given data
*The given mass is m = 0.520 kg
*The spring stretches at a distance is x = 18.7 cm = 0.187 m
*The value of the acceleration due to gravity is g = 9.8 m/s^2
(a)
The formula for the spring constant of the spring is given as
[tex]\begin{gathered} F=kx \\ mg=kx \\ k=\frac{mg}{x} \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} k=\frac{(0.520)(9.8)}{(0.187)} \\ =27.2\text{ N/m} \end{gathered}[/tex]Hence, the spring constant of the spring is k = 27.2 N/m
(b)
The formula for the frequency of its
What is the difference in the path of a ball tossed straight up in the air by a passenger on a a bus from the view point of the passenger, and the person on the street?
The difference in the path of a ball tossed straight up in the air by a passenger on a a bus from the view point of the passenger, and the person on the street is that the ball would appear to the passenger to be making an up and down movement when the ball is thrown up, while the stationary observer will actually see the ball moving along a parabolic path.
What is a parabolic path?A parabolic path is described as a Kepler orbit with the eccentricity equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic.
The Parabolic path is also defined as the angle of trajectory of a projectile.
Learn more about parabolic path at: https://brainly.com/question/16791942
#SPJ1
A man takes in 0.95 × 107 J of energy each day from consuming food, and maintains a constant weight. what power in watt supplied by the food?
Given data
*The given energy is E = 0.95 × 10^7 J
*The given time is t = 1 day = (24 × 60 × 60) s = 86400 s
The formula for the power in watt supplied by the food is given as
[tex]P=\frac{E}{t}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} P=\frac{(0.95\times10^7)}{(86400)} \\ =1.09\times10^2\text{ W} \end{gathered}[/tex]Hence, the power in watt supplied by the food is P = 1.09 × 10^2 W
Sodium has a density of 1.95 g/cm3. What is the volume of 56.2 g of sodium?
Answer: couldn't type in that little 3 haha
Explanation:
A 228-turn, 24.506-cm-diameter coil is at rest in a horizontal plane. A uniform magnetic field 27 degrees away from vertical increases from 0.807 T to 4.68 T in 13.843 s. Determine the emf induced in the coil.
Given:
• Number of turns, N = 228
,• Diameter, d = 24.506 cm
,• θ = 27 degrees
,• Initial Magnetic field, B1 = 0.807 T
,• Final, B2 = 4.68 T
,• Time , t = 13.843 s
Let's find the induced emf in the coil.
To find the induced EMF, apply Faraday's law:
[tex]\begin{gathered} E=N\frac{d}{dt}(B*A) \\ \\ E=N*Acos\theta\frac{d}{dt}(B) \\ \\ E=N*(\pi r^2)cos\theta(\frac{B_2-B_1}{t}) \end{gathered}[/tex]Where:
A is the area in meters.
Rewrite the diameter from cm to meters.
Where:
100 cm = 1 meters
24.056 cm = 0.24506 m
Now, the radius will be:
radius = diameter/2 = 0.24506/2 = 0.12253 m
Now, plug in the values and solve for E:
[tex]\begin{gathered} E=228*(\pi *(0.12253)^2)cos(27)*(\frac{4.68-0.807}{13.843}) \\ \\ E=228*0.0471666*cos(27)*0.27978 \\ \\ E=2.6\text{ volts} \end{gathered}[/tex]Therefore, the EMF induced in the coil is 2.6 volts.
ANSWER:
2.6 v
What is troubling about the circumstance when a coil is stationary and a magnet moves as compres to when a magnet is stationary and the coil moves?
When the magnet is moved, the galvanometer needle will deflect. It shows that the current is flowing in the coil. When the magnet moves into the coil, the needle deflects into one way, and if the magnet moves out of the coil, the needle deflects into the other way.
When the magnet is held stationary near, or even inside, the coil, no current will flow through the coil.
what is the mass on grams of 0.56 moles of NaCl
Answer:
1 mole of Na = 23 g
1 mole of Cl = 35 g
1 mole of NaCl = 58 g
.56 * 58 g = 32.5 g
As the speed of an object falling toward Earth increases, the gravitational potential energy of the object with respect to EarthA. IncreasesB. DecreasesC. Remains the same
Answer:
B. Decreases
Explanation:
When an object is falling toward Earth, the height of the object decreases, and the speed increases. Then, the gravitational potential energy decreases, and the kinetic energy increase because the first one depends on the height and the second one depends on the speed. Therefore, the answer is:
B. Decreases
An unbanked asphalt highway has turns of 40m radii. How fast should the speed limit be if cars may be traveling in the rain? (Us for wet asphalt on rubber is .755)
Given data:
* The radius of the turn is r = 40 m.
* The coefficient of friction is,
[tex]\mu_s=0.755[/tex]Solution:
The centripetal force acting on the car is,
[tex]F=\frac{mv^2}{r}[/tex]where m is the mass of the car,
The frictional force acting on the car is,
[tex]F_r=\mu_smg[/tex]where g is the acceleration due to gravity,
In order to travel a car in rain, the centripetal force acting on the car must be equal to the frictional force on the same car.
Thus,
[tex]\begin{gathered} F_r=F_{} \\ \mu_smg=\frac{mv^2}{r} \\ \mu_sg=\frac{v^2}{r} \\ v^2=r\mu_sg \end{gathered}[/tex]Substituting the known values,
[tex]\begin{gathered} v^2=0.755\times40\times10 \\ v^2=302 \\ v=17.4\text{ m/s} \end{gathered}[/tex]Thus, the maximum speed limit of the car in rain is 17.4 m/s.
Hence, the nearest possible correct answer is option b.
A string with both ends fixed is vibrating in its second harmonic. The waves have a speed of 36m/s and a frequency of 60Hz. The amplitude of the standing wave at an antinode is 0.6cm. calculate the amplitude of the motion of points on the string a distance of 30cm,15cmand 7.5cm on the left hand end of the string.
The amplitude of the motion of points on the string a distance of 30cm,15cmand 7.5cm is 0.0547m, 0.027m and 0.0137m respectively.
Amplitude is the maximum range of vibration or oscillation, measured from the equilibrium position
According to the equation of the second harmonic motion
A = sin (kx)
A = Amplitude
k = [tex]\frac{2\pi f}{v}[/tex] = [tex]\frac{2*\pi * 60}{36}[/tex] = 10.467
x = distance of the point
For x = 30 cm = 0.3 m
A = sin (kx)
A = Sin (10.467 * 0.3)
A = 0.0547 m
For x = 15 cm = 0.15 m
A = sin (kx)
A = Sin (10.467 * 0.15)
A = 0.027 m
For x = 7.5 cm = 0.075 m
A = sin (kx)
A = Sin (10.467 * 0.075)
A = 0.0137 m
To know more about amplitude,
https://brainly.com/question/15518312
#SPJ1
When you eat cereal and thenlift weights, how is the energytransformed?A. The chemical energy in the cereal istransformed into mechanical energy.B. The thermal energy in the cereal istransformed into mechanical energy.C. The mechanical energy in the cereal istransformed into chemical energy.
in any food not just in cereal there are chemical energy is stored in the form of
carbon, protein, fats, etc.
when we eat the food our body transforms this energy into
energy by decomposing the food into its elementary
particles and store it in the form of chemical energy and when we need energy
to do work it (body) coverts the energy into the mechanical energy by various
process.
so the correct answer is option (A)
ine? Bir10. Two people are pulling on opposite ends of a rope so that ithas a tension of 150 newtons. If the rope is not moving, withwhat pulling force is each of the two people pulling?
ANSWER
150 N
EXPLANATION
The rope is not moving, so the net force on it is 0. The force that each person exerts on the rope is equal and opposite to the tension on the rope, so the sum of the forces acting on it is zero.
Hence, the force that each of the two people is exerting on the rope while pulling is 150 Newtons.
A basketball player jumps for a rebound and reaches a maximum height of 1.5 m. with what speed did he jump off the floor? How long was he in the air?
The final speed of the player can be given as,
[tex]v^2=u^2-2gh[/tex]At the maximum height, the final speed of player is zero.
Plug in the known values,
[tex]\begin{gathered} (0m/s)^2=u^2-2(9.8m/s^2)(1.5\text{ m)} \\ u^2=29.4m^2s^{-2} \\ u=5.42\text{ m/s} \end{gathered}[/tex]Thus, the speed with which it jump off the floor is 5.42 m/s.
The time for which the player was in player is,
[tex]t=\sqrt[]{\frac{2h}{g}}[/tex]Plug in the known values,
[tex]undefined[/tex]
5. Draw a transverse wave with two wavelengths and label amplitude, crest, trough, and
equilibrium position.
A wave is considered to be transverse if its oscillations run counterclockwise to the wave's direction of advance. A longitudinal wave, on the other hand, moves in the direction of its oscillations. Transverse waves include water waves.
A waveform signal's wavelength, which is the distance between two identical locations (adjacent crests) in the succeeding cycles, determines whether it is sent through space or via a wire. This length is typically defined in wireless systems in metres (m), centimetres (cm), or millimetres (mm).
The largest displacement or distance made by a point on a wave or vibrating body relative to its equilibrium position is its amplitude. It is equal to one-half of the vibration path.
The crest and trough of a wave, respectively, are its highest and lowest surface portions. The wave height is the vertical distance between the peak and trough. The wavelength is the horizontal separation between two consecutive crests or troughs.
The horizontal line at the wave's centre stands in for balance. A period is the length of time it takes to complete a cycle, which includes travelling from one peak to another, from one trough to another, or from one equilibrium point to another (both equilibrium points same direction).
To know more about transverse wave, click on the link below:
https://brainly.com/question/12584334
#SPJ9
if you had only one telescope and wanted to take both visible-light and ultraviolet pictures of stars, where should you locate your telescope?
If we just had one telescope and wanted to photograph stars in both visible and ultraviolet light, we should put it in space.
While visible light is observable from Earth, ultraviolet light can only be seen from space. Indeed, Hubble's ability to observe ultraviolet light gives it a major advantage over larger ground-based observatories.
Rank the visible light hues from left to right according to the altitude in the atmosphere where they are totally absorbed. All visible light wavelengths reach the Earth's surface, which is why we can see all colors and why visible-light telescopes perform well on the ground.
Visit the link below to learn more about the telescope:
brainly.com/question/26526281
Determine the speed of the Earth in its motion around the Sun using Newton's Law of Universal Gravitation and centripetal force. Look up the values of the Earth's mass, the Sun's mass, and the average distance of Earth from the Sun; other than G, nothing else is needed
In order to determine the speed of the Earth, proceed as follow:
Consider that the centripetal force must be equal to the gravitational force between the Earth and the Sun (because guarantees the stability of the system):
[tex]F_g=F_c[/tex]Fg is the gravitational force and Fc the centripetal force. The expressions for each of these forces are:
[tex]\begin{gathered} F_g=\text{G}\frac{\text{mM}}{r^2} \\ F_c=ma_c=m\frac{v^2}{r} \end{gathered}[/tex]where,
G: Cavendish's constant = 6.67*10^-11 Nm^2/kg^2
m: Earth's mass = 5.97*10^24 kg
M: Sun's mass = 1.99*10^30kg
v: speed of Earth around the Sun = ?
r: distance between the center of mass of Earth and Sun = 1.49*10^8km = 1.49*10^11 m
Equal the expressions for Fg and Fc, solve for v, replace the previous values of the parameters and simplify:
[tex]\begin{gathered} \text{G}\frac{\text{mM}}{r^2}=m\frac{v^2}{r} \\ v^{}=\sqrt[]{\frac{GM}{r}} \\ v=\sqrt[]{\frac{(6.67\cdot10^{-11}N\frac{m^2}{\operatorname{kg}^2})(1.99\cdot10^{30}kg)}{1.49\cdot10^{11}m}} \\ v\approx29846.7\frac{m}{s} \end{gathered}[/tex]Hence, the speed of the Earth around the Sun is approximately 29846.7m/s
Below is a diagram of a 5.0 kg block being dragged to the right, along a horizontal surface. The
coefficient of dynamic friction, is 0.40. Take acceleration due to gravity, g, as 9.81 ms ².
5 kg
30. N
What is the acceleration of the block? Give your answer correct to two significant figures, in
m-s-2, without units.
The acceleration of the block when the coefficient of friction is 0.40 is 3.924 m/s².
The ratio of the frictional resistive force to the perpendicular force pushing the objects together is known as the coefficient of friction.
Acceleration is the rate at which an object's velocity with respect to time changes.
The block of mass 5 kg is dragged to the right on a horizontal surface.
The coefficient of friction is 0.40.
The acceleration due to gravity is 9.81 m/s².
The force on the block is 30 N.
Now, the force is defined as the product of the mass and acceleration of the object.
Now, using the conservation of force:
F = μmg
ma = μmg
a = μg
a = 0.40 × 9.81
a = 3.924 m/s²
Learn more about coefficient of friction here:
brainly.com/question/23971360
#SPJ1
Four masses are arranged as shown. They are connected by rigid, massless rods of lengths 0.780 m and 0.500 m. What torque must be applied to cause an angular acceleration of 0.750 rad/s2 about the axis shown?
Given,
The length of the rods;
L=0.780 m
l=0.500 m
The angular acceleration, α=0.750 rad/s²
The masses;
m_A=4.00 kg
m_B=3.00 kg
m_C=5.00 kg
m_D=2.00 kg
The moment of inertia of the given system of masses is given by,
[tex]\begin{gathered} I=\Sigma mr^2 \\ =m_A(\frac{L}{2})^2+m_B(\frac{L}{2})^2+m_C(\frac{L}{2})^2+m_D(\frac{L}{2})^2 \\ =(\frac{L}{2})^2(m_A+m_B+m_C+m_D) \end{gathered}[/tex]Where r is the distance between each mass and the axis of rotation.
On substituting the known values,
[tex]\begin{gathered} I=(\frac{0.780}{2})^2(4.00+3.00+5.00+2.00) \\ =2.13\text{ kg}\cdot\text{m}^2 \end{gathered}[/tex]The torque required is given by,
[tex]\tau=I\alpha[/tex]On substituting the known values,
[tex]\begin{gathered} \tau=2.13\times0.750 \\ =1.6\text{ Nm} \end{gathered}[/tex]Thus the torque that must be applied to cause the required acceleration is 1.6 Nm
A fireman standing on a 14 m high ladderoperates a water hose with a round nozzle ofdiameter 2.65 inch. The lower end of the hose(14 m below the nozzle) is connected to thepump outlet of diameter 3.49 inch. The gaugepressure of the water at the pump isCalculate the speed of the water jet emerg-ing from the nozzle. Assume that water is anincompressible liquid of density 1000 kg/m3and negligible viscosity. The acceleration ofgravity is 9.8 m/s?Answer in units of m/s.
Given data,
The height, H = 14 m
The diameter, D = 2.65 inch
The gauge pressure, P = 317.84 kPa
We need to calculate the speed of the water jet emerging from the nozzle.
Using Bernoulli's equation,
[tex]\begin{gathered} \frac{1}{2}\rho(v^2_n-v^2_p)=P_{gauge\text{ }}-\rho gh \\ (v^2_n-v^2_p)=(\frac{2}{\rho})P_{gauge}-2gh \\ v^2_n-(\frac{A_n}{A_p})^2v^2_n=(\frac{2}{\rho})P_{gauge}-2gh \\ v^2_n-(\frac{r_n}{r_p_{}})^4v^2_n=(\frac{2}{\rho})P_{gauge}-2gh \end{gathered}[/tex]Further solved as,
[tex]\begin{gathered} v_n=\sqrt[]{\frac{(\frac{2}{\rho})P_{gauge}-2gh}{1-(\frac{r_n}{r_p})^4}} \\ v_n=\sqrt[]{\frac{(\frac{2}{1000})\times317.84\times10^3-2\times9.8\times14}{1-(\frac{1.325_{}}{1.745_{}})^4}} \\ v_n=\sqrt[]{\frac{635-274.4}{0.667}} \\ v_n=\sqrt[]{540.62} \end{gathered}[/tex]Thus, the speed of the water jet is
[tex]v=23.25\text{ m/s}[/tex]g) 0.35 oz to mgh) 75 mL to gali) 54 mi to kmj) 1789 ft to km
In order to covnert the given quantities, use the correct covnersion factor, as follow:
g) 0.35 oz to mg
[tex]0.35oz\cdot\frac{28.3495g}{1oz}\cdot\frac{1000mg}{1g}=9922.325mg[/tex]h) 75 mL to gal
[tex]75mL\cdot\frac{1L}{1000mL}\cdot\frac{0.2641722gal}{1L}\approx0.02gal[/tex]i) 54 mi to km
[tex]54mi\cdot\frac{1.61\operatorname{km}}{1mi}=86.94\operatorname{km}[/tex]j) 1789 ft to km
[tex]1789ft\cdot\frac{0.3048m}{1ft}\cdot\frac{1\operatorname{km}}{1000m}\approx0.54\operatorname{km}[/tex]