The sine components of the velocity of the boat will balance out the velocity of the river making an angle of 37° with the vertical.
What are the components of vectors?Every vector can be broken into some components, these components on vector addition would again give the resultant vector.
The components of the vector act independently.
Given:
Velocity of the boat in still water = 20km/h
Velocity of the river stream= 12km/h
We want the boat to go directly opposite to the starting point without any drift. For this one component of the boat's speed should be acting parallel to the speed of the stream and cancelling its effect in the motion of the boat.
Therefore preventing the drift of the boat now with the other perpendicular speed vector component the boat will cross the river.
Assumption:
The boat goes at an angle p with the vertical or perpendicular to the river stream.
v is the resultant speed of the boat
u is the velocity of the stream
According to the question:
v × sin(p) = u
Sin(p) = 0.6
p = 37°
Therefore, The sine components of the velocity of the boat will balance out the velocity of the river making an angle of 37° with the vertical.
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For an object in uniform circular motion, its velocity and acceleration vectors are always perpendicular to each other at every point in the path. True or false?.
For an object in uniform circular motion, its velocity and acceleration vectors are always perpendicular to each other at every point in the path is true.
What is circular motion?Circular motion refers to the movement of a body part around the perimeter of a circle or in a circular motion. It may rotate at a fixed speed and angular rate or it may rotate at a variable rate, making it either uniform or non-uniform. A three-dimensional body's components move in circles as it rotates around a fixed axis. The center of mass of a body moves according to the equations of motion. In circular motion, the distance between the body and a fixed point on the surface stays constant.
Examples of circular motion include an artificial satellite circling the Earth at a constant altitude, ceiling fan blades spinning around a hub, and a rotating disc.
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A plane convex lens is made of glass (n = 1.5) with one flat surface and the other having a radius of 20 cm. what is the focal length (in cm) of the lens?
The calculated value is 5:2.
The reciprocal of the focal length is used to calculate a lens's power. In diopter's, lens power is expressed (D). Positive focal lengths and positive power values are characteristics of convergent (convex) lenses. Negative focal lengths and negative power values are characteristics of diverging (concave) lenses.
Given that a N l =1.25 and a Ng =1.5
The focal length of a glass (g) lens in a medium (m) may be calculated using the formula
f1= (mNg 1) [1/R1/ 1/R2].
fa1 = (aNg1) [1/R1/ 1/R 2] while the lens is in the air.
When the lens is submerged in liquid, f l1 = (aNg 1) [1/R 1/1/R2] =1.5/1.25, which divides equation 1 by equation 2, and
fi/fa = (1.5/1.251)/ (1.51)
=5/2 or
Pa / Pi = 5/2 (since f=1/P).
Therefore, Pa:Pi= 5:2.
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Sometimes scientists gather information that contradicts accepted theories or explanations. if the new information is replicated many times, the accepted theory that it contradicts will often be updated or modified to reflect the new information. based on this, it can be determined that scientific knowledge is durable in part because a. new information on accepted theories is never discovered. b. experiments are never performed more than once. c. scientists ignore information that contradicts accepted theories. d. it is open to change as new information is learned.
Scientists occasionally gather data that deviates from conventional ideas or interpretations. The widely held idea that the new information contradicts will frequently be revised or changed to take into account the new information if it is repeatedly verified.
Empirical evidence is the foundation of scientific knowledge. It is strong and lasting since it is the end product of all the prior study and testing that was done. But science also acknowledges that all of this information is a product of human endeavor and that it may contain numerous errors. Therefore, once a new idea is discovered and repeatedly confirmed, scientific knowledge is adaptable enough to take it into account and evolve.
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The temperature of an ideal monatomic gas rises by 8.0 k. what is the change in the internal energy of 1 mol of the gas at constant volume?
The change in the internal energy of 1 mol of the gas at constant volume is 100J
What is internal energy?The energy contained within a thermodynamic system is referred to as its internal energy. Internal energy is constant in an isolated system. It is the energy required to build or prepare the system in the internal state that it is in at the time.
The kinetic energy of individual particles within the system is included, but not the kinetic energy of motion of the system as a whole. It records the system's energy gains and losses that result from modifications to its internal state. It is impossible to directly quantify internal energy. It is determined by comparing the difference to a conventional state-defined reference zero.
We know that, change in internal energy at constant volume is given by
[tex]dE_{int}[/tex] = n × Cv × dT
Here, n = no. of moles
Cv = molar heat capacity
dT = temperature difference
Applying the equation on the question, we get
[tex]dE_{int}[/tex] = 1 mol × 12.47 J/mol k × 8k
= 99.76 J ≈ 100J
Hence, the change in internal energy during the process is 100 J
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if the temperature remains the same but the wind speed increases, the wind chill index will increase stay the same decrease
The wind chill index will increase, if the temperature remains the same but the wind speed increases.
What is wind?Wind is the customary improvement of air or various gases near with a planet's surface. Turns occur on an extent of scales, from whirlwind streams persevering through a few minutes, to neighborhood breezes made by warming of land surfaces and persevering through two or three hours, to overall breezes coming about as a result of the differentiation in maintenance of daylight based energy between the climate zones in the world. The two essential drivers of tremendous degree natural scattering are the differential warming between the equator and the posts, and the turn of the planet (Coriolis influence). Inside the wildernesses and subtropics, warm low streams an over area and undeniable levels can drive rainstorm dispersals. In ocean front areas the sea breeze/land breeze cycle can describe close by breezes; in locales that have a variable area, mountain and valley breezes can win.
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a baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher. at what point is the magnitude of the acceleration at a minimum? (air resistance is negligible)
At the maximum height ( top ) position, the ball's speed is minimum so at this point the magnitude of the acceleration at a minimum.
What is acceleration?In mechanics, acceleration is the rate at which the velocity of an object changes in relation to time. Acceleration is vector quantity (in that they have magnitude and direction). The direction of the net force acting on an object determines its acceleration. the extent of an object's acceleration as per Newton's Second Law. Such negative accelerations are typically produced by retrorocket burning in spacecraft. Since both acceleration and deceleration are changes in velocity, they are considered equally. Passengers experience each of these accelerations (tangential, radial, and deceleration) until their relative (differential) velocities are equal to the acceleration caused by the change in speed.
At most extreme level position the upward part of speed is generally zero. By then the ball just has level speed and minimum magnitude of acceleration.
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find the strength of the net force produced by a 34-n force and a 21-n force in each of these cases.
The net force is in the first case is 13 N and in the second case is 55 N.
What is gravitational force?All mass-bearing objects are attracted by gravitational force. Because it consistently attempts to bring masses together rather than push them apart, the gravitational force is referred to as attractive.
As we know, the gravitational force is given by:
[tex]\rm F = \dfrac{Gm_1m_2}{r^2}[/tex]
Where G is the gravitational constant.
m1 and m2 are masses.
r is the distance between the masses.
It is given that:
Two forces are given:
The two forces act in opposite directions:
= 34 - 21
= 13 N
Both forces act in the same direction:
= 34 + 21
= 55 N
Thus, the net force is in the first case is 13 N and in the second case is 55 N.
The question is incomplete the complete question is:
find the strength of the net force produced by a 34-n force and a 21-n force in each of these cases.
The two forces act in opposite directions.
Both forces act in the same direction.
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An athlete leaves the base camp and hikes 10 km, north and then hikes 5 km east. Determine his resulting displacement.
5km East
125km NE
15 km SE
11.2 km NE
Answer: 11.2
Explanation:
The scatter plot for a set of x and y values shows the data points clustered in a nearly perfect circle. for these data, what is the most likely value for the pearson correlation?
Answer is Zero.
By multiplying the standard deviation of one variable (x) by the standard deviation of the other variable, the Pearson correlation coefficient, denoted by the symbol r, is calculated.
A scatter plot diagram is a graphic representation of data where these two variables are simultaneously observed.
The two variables x and y grow in x when y increases, which is referred to as having a positive slope in a positive correlation.
On the other hand, the correlation between x and y is said to be negative and the accompanying regression line has a negative slope when there is an increase in x and a drop in y. On rare occasions, x and y may not seem to be related. Accordingly, the scatter plot diagram's data typically form a nearly perfect circle and are considered to have zero correlation.
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by what percentage do the transferred electrons change the mass of the penny? (express your result as a positive percentage for an increase, negative for a decrease.)
The mass of the coin will decrease after the electrons are transferred and it will decrease by a percentage of -
[- (n x 9.1 x 10⁻³¹) / m] x 100
We have a Penny (Coin) from which some electrons are transferred
We have to determine by what percentage do the transferred electrons change the mass of the penny.
What is Charge?The sufficiency or deficiency of electrons leads to the development of charge.
According to the question -
Assume the mass of penny when no electrons are transferred is m kg.
Now, suppose you rubbed the coin against your hand and the coin lost some of its electrons. Let this number be n. Now, the mass of electron is 9.1 × [tex]10^{-31}[/tex] kilograms.
The total mass in kilograms lost will be -
(n x 9.1 × 10⁻³¹) Kg
Therefore - the total mass of coin after loosing electrons will be →
m - (n x 9.1 × 10⁻³¹ ) Kg
There will be decrease in the mass of the penny. The amount of decrease in mass will be → final mass - initial mass =
m - (n x 9.1 × [tex]10^{-31}[/tex]) - m = - (n x 9.1 × [tex]10^{-31}[/tex]).
This negative sign indicates that the mass has decreased.
Hence, the mass of the coin after transferring the electrons will decrease and it will decrease by percentage of →
[- (n x 9.1 x 10⁻³¹)/m] x 100
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1. In 10 seconds a car accelerates 4m/s2 to 6 m/s. How fast was the car going before it accelerated?
2. An object at rest starts accelerating. If it travels 10 meters to end up going 20 m/s, what was its acceleration?
3. A car stops in 150 m. If it has an acceleration of –8m/s2, how long did it take to stop?
4. An object is thrown up into the air going 100 m/s. How fast is it going 1.5 seconds later?
5. A rock falls off a cliff and falls for 1 secs. How high is the cliff?
6. A person throws tennis ball 2 m/s straight up. How long does it take for it to come back to their hand?
7. A ball goes 400 m in 4 seconds. If was moving 10 m/s to begin with, what is its final velocity?
The results of the calculation are;
1) The acceleration is 0.2 m/s^2
2) The acceleration is 20 m/s^2
3) Can not be solved as the parameters are not complete
4) Has a final velocity of 114.7 m/s
5) The height is 4.9 m
6) The total time taken is 0.4 s
7) The final velocity is 190 m/s
What is the acceleration?The term acceleration is defined as the rate of change of the velocity with time. We shall now look at the solution to each of the problems.
1) Using;
v = u + at
v = final velocity
u = initial velocity
a = acceleration
t = time
a = v - u/t = 6 - 4/10
a = 0.2 m/s^2
2) v^2 = u^2 + 2as
s = distance
u = initial velocity
a = acceleration
v =final velocity
Given that it started from rest u = 0 m/s
v^2 = 2as
a = v^2/2s
a = (20)^2/ 2 * 10
a = 20 m/s^2
3) This problem can not be solved because the initial velocity is missing
4) v = u + gt
v = 100 + (9.8 * 1.5)
v = 114.7 m/s
5) h = ut + 1/2 gt^2
Since it was dropped from a height u = 0 m/s
h = 1/2 gt^2
h = 0.5 * 9.8 * (1)^2
h = 4.9 m
6) v = u + gt
At the maximum height v = 0 m/s
u = gt
t = u /g
t = 2/9.8
t = 0.2 s
To go up and come back 2(0.2) = 0.4 s
7) s = ut + 1/2 at^2
400 = (10 * 4) + 0.5 * (4)^2 * a
400 = 40 + 8a
400 - 40/8 = a
a = 45 m/s^2
Using;
v = u + at
v = 10 + 45 * 4
v = 190 m/s
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What is the term for the property of sound that gives instruments and voices their unique tone color?
The term for the property of sound that gives instruments and voices their unique tone color is timbre.
different names for timbre include tone colour and tone first-rate.
the arena is home to a extensive form of musical units.
every tool differs from every other tool by having a unique sound or tone coloration.
A musical tool's awesome sound pleasant that sets it apart from other gadgets is called the tone coloration or timbre and is unrelated to pitch, rhythm, or quantity.
The definition of tone colour and tone first-rate, which can be often used interchangeably, are fairly similar.
The intrinsic sound features of any device that satisfactory characterise the tone colour in tune are known as tone best.
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calculate a. how long it took for king kong to fall straight down from the top of the empire state building (380 m) and b. his velocity just before landing.
(a) King kong will fall straight from the top of the empire state building in 8.81 s.
(b) The velocity of king kong before landing is 86.3 m/s.
What is the acceleration due to gravity?
The longer an object is in free fall, the faster it descends toward the ground due to gravity. In actuality, an object's velocity rises by 9.8 m/[tex]s^{2}[/tex], so it reaches 9.8 m/s by the time it begins to fall.
Time taken for king kong to land on the ground from the Empire state building is
[tex]$$t=\sqrt{\frac{2 h}{g}}\\=\sqrt{\frac{2(380 \mathrm{~m})}{9.8 \mathrm{~m} / \mathrm{s}^2}}[/tex]
= 8.81 s
(b)
The velocity of the king kong when it touches the ground is
[tex]$$v=\sqrt{2 g h}\\=\sqrt{2\left(9.8 \mathrm{~m} / \mathrm{s}^2\right)(380 \mathrm{~m})}[/tex]
=86.3 m/s
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we investigated a jet landing on an aircraft carrier. in a later maneuver, the jet comes in for a landing on solid ground with a speed of 87 m/s, and its acceleration can have a maximum magnitude of 8.55 m/s2 as it comes to rest. (a) from the instant the jet touches the runway, what is the minimum time interval needed before it can come to rest? (b) can this jet land on a small tropical island airport where the runway is 0.800 km long? (c) explain your answer.
(a) The minimum time interval needed before it can come to rest is t = 10.17 sec for a jet which is travelling at a a speed of 87 m/s, and its acceleration can have a maximum magnitude of 8.55 m/s2
(b) yes the jet can land on a small tropical island airport where the runway is 0.800 km long.
(c) The jet is safe to land.
What is acceleration?Acceleration is the rate at which an object's velocity with respect to time changes. It is a vector quantity to accelerate (in that they have magnitude and direction). The direction of the net force acting on an object determines the direction of its acceleration. According to Newton's Second Law, an object's acceleration is the result of two factors working together: the object's mass, which varies depending on the materials it is made of, and the net balance of all external forces acting on it. The magnitude of an object's acceleration is inversely proportional to the object's mass.
The SI unit for acceleration is [tex]m/sec^{2}[/tex].
Use the formula to calculate the time required to stop the jet
v = u + at
0 = 87 + (-8.55)t
t = [tex]\frac{87}{8.55}[/tex]
t = 10.17 sec
Use the following formula to calculate the distance travelled by the jet is,
[tex]x = ut + \frac{1}{2} at^{2}[/tex]
= [tex]( 87 \times 10.17) + \frac{1}{2} (-8.55) (10.17)^{2}[/tex]
= 884.79 - 884.31
=.48m
Yes, the can land on a small tropical island airport where the runway is 0.800 km long.
The jet is safe to land.
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A ball is launched at some angle from horizontal toward a target some distance away on the ground. Neglect any effects due to air resistance. Where would the speed of the ball be the slowest?.
Answer:
you get yet?
Explanation:
Answer:At the place where it is when acceleration is the least.
Explanation:
I believe it is this answer. At launch the speed is the slowest because as it is falling the acceleration increases.
21 What happens to the molecules of a gas when the gas changes into a liquid?
A They move closer and lose energy.
B They move closer and gain energy.
с They move apart and lose energy.
D They move apart and gain energy.
the electric field midway between two equal but opposite point charges is 573 n/c , and the distance between the charges is 16.0 cm
The charge will be equal to 4.07 x 10⁻¹⁰ coulombs.
What is an electric field?The term "electric field" refers to the physical field that surrounds electrically charged particles and pulls or attracts all other charged particles nearby.
Use the following formula E = Kq / r² Since the electric field is 573 N/C
The distance of the midpoint of the charge.
r = 1/2 x 16 = 8 cm = 0.08m.
573 = (8.998 x 10⁹) x q) / (0.08)²
573 x 0.0064 = 8.998 x 10⁹ x q
q = (573 x 0.0064)/ 8.998 x 10^(9)
q =3.6672 / 8.998 x 10⁹
q = 4.07 x 10⁻¹⁰ coulombs
Therefore, the charge will be equal to 4.07 x 10⁻¹⁰ coulombs.
The complete question is given below:-
The electric field midway between two equal but opposite point charges is 573 n/c , and the distance between the charges is 16.0 cm. Calculate the magnitude of the charge.
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A lightning bolt with 10 ka strikes an object for 15 s. how much charge is deposited on the object?
The charge deposited on the object is 150000 C.
What is charge?Charge can be defined as the product of current and time. The S.I unit of charge is coulombs (C.)
To calculate the charge deposited on the object, we use the formula below
Formula:
Q = it.................equation 1Where:
Q = Chargei = Currentt = TimeFrom the question,
Given:
i = 10 kA = 10000 At = 15 sSubstitute these values into equation 1\
Q = 10000×15Q = 150000 CHence, the charge deposited on the object is 150000 C.
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The n-h bond in the ammonium ion, nh 4, is formed by the overlap of what two orbitals? sp2-s sp3-sp2 sp3-sp3 sp2-sp2 sp3-s
sp3-s
In the ammonium ion , 2s and 2p orbitals create four sp3 hybrid orbitals. Three form covalent bonds with hydrogen. The fourth sp3 orbital has a non bonding lone pair of electrons, which can create ammonium ion.
Amonium Ion is NH4+1Ammonium Ion is called Alkaline AirAmmonium Ion is a olourless gas with a strong pungent odor and very soluble in water and ether. it is a polar compoundAmmonium Ion has a strong irritating action on the mucous membranes of the eyes, nose, and throat.If ammonium is produced then a pungent smelling gas is produced, turns damp red litmus blue during lab test.To know more ammonium ion visit : https://brainly.com/question/11173657
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What’s an example of potential energy? I WILL CROWN YOU PLS HELP
A
Water behind a dam
B
A dart stuck in a dartboard
C
Plants using photosynthesis
D
A cow chewing grass
Answer:
I think it's A
Explanation:
potential energy is energy waiting to move right?
Use physics to find the magnitude (actual value) of the electric field at thelocation of the yellow dot.
The Magnitude of the electric field intensity at the location of yellow dot will be -
E = Q/4πε₀Kr²
We have a Yellow dot situated at distance of r meters from the charge.
We have to find the magnitude of Electric field at this Yellow dot.
What is Electric Field of a Charge?The electric field of a charge is the region around the charge in which the influence of charge's electrostatic force can be felt or measured.
According to the question -
Assume that the Yellow dot is at distance 'r' meters apart from the Point charged particle Q. Now, the Electric field intensity at the yellow dot distanced 'r' meters apart will be -
E = Q/4πε₀Kr²
The above formula will give the intensity at the yellow dot. Since the source charge is positive, therefore the direction of the electric field will be away from the charge.
Hence, the Magnitude of the electric field intensity at the location of yellow dot will be -
E = Q/4πε₀Kr²
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If the precessional frequency of the protons net magnetization is approximately 21.3 mhz, what would be the magnetic strength used to spatial localize a slice?
The correct option is (c) 0.5 .
The magnetic field experienced by the patient's protons is 0.5 Tesla.
What is a magnetic field in simple terms?
The area in which the force of magnetism acts around a magnetic material or a moving electric charge is known as the magnetic field. A diagram that shows the magnetic field and how a magnetic force is distributed inside and outside of a magnetic substance.
What causes a magnetic field?While opposite poles (north and south) are drawn to one another, the same poles repel one another. The north-seeking poles of the iron's atoms line up in the same direction when it is rubbed against a magnet. A magnetic field is produced by the force that the aligned atoms produce.
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The complete question is:
"If the precessional frequency of the protons net magnetization is approximately 21 MHz, a ____ Tesla magnetic field is being experienced by the patient's protons?
(a) 2.0
(b) 1.5
(c) 0.5
(d) 0.3"
(a) if the maximum accelerationthat is tolerable for passengers in asubway train is 1.34 m/s2and subwaystations are located 806 m apart, whatis the maximum speed a subway traincan attain between stations?
Complete question
If the maximum acceleration that is tolerable for passengers in a subway train is 1.34m/s
2
and subway stations are located 806m apart, what is the maximum speed a subway train can attain between stations?
From rest, the train is assumed to accelerate at a rate [tex](v_{0} =0)[/tex] and [tex](x_{0}=0)[/tex] of [tex]1 = 1.34m/s^{2}[/tex] until it reaches the halfway point, then decelerates at a rate [tex]2 = 1.34 m/s^{2}[/tex] until it stops [tex](v_{2}=0)[/tex] at the following station. The distance between the two stations (l = 806m).
maximum speed refers back to the fastest rate of speed someone can reap. while athletes regulate the significance (how speedy they may be moving) or path (or each) in their movement, or both, their acceleration adjustments as properly when you consider that acceleration is related to pace, which has both a importance and a path related with it.
Given data:
The midpoint's velocity [tex]V_{1}[/tex] is experienced at:
[tex]x = \frac{1}{2} = \frac{806}{2} =403 m[/tex]
Then,
⇒ [tex]\mathrm{V}_{1}^{2}=\mathrm{V}_{0}^{0}+2a_{1} x[/tex]
⇒ [tex]v_{1} =\sqrt{0+2*1.34*403}m/s[/tex]
= 32.86 m/s
Thus, the maximum speed attained is 32.86 m/s.
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What happens to a satellite not moving fast enough to stay in orbit 
Answer:
It would crash into the thing it's orbiting.
Explanation:
Since it's not going fast enough to counter the pull of gravity.
If the mass of a sliding block is tripled while a constant net force is applied, by how much does the acceleration change?.
The acceleration of the block will be 1 / 3 times.
What is acceleration?Acceleration of any object is defined as the variation in the speed of the object with the variation of the time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of the acceleration can be m / sec², miles / sec², etc.
Given that the mass of a sliding block is tripled while a constant net force is applied. The acceleration of the block will be calculated as below:-
F = Mass x Acceleration
F = 3 Mass x Acceleration
Here to make the force constant the acceleration has to be divided by 3.
Therefore, the acceleration of the block will be 1 / 3 times.
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how far would it be from the milky way galaxy to the most distant galaxies in the observable universe on this scale?
The distance from the milky way galaxy to the most distant galaxies in the observable universe would be approximately 1.34 kilometers on a scale in which the MIlky Way Galaxy was the size of a marble(about 1 cm).
The MIlky Way is the galaxy that includes our solar system along with billions of stars.
To measure distances in space, we use the unit light year. One light year is the distance travelled by light in year. 1 light year is equal to 9.5 trillion km.
The size of MIlky Way is about 1,00,000 light years and the distance from the MIlky Way to the most distant galaxies in the observable is 13.4 billion light years.
Therefore, the distance from the milky way galaxy to the most distant galaxies in the observable universe would be approximately 1.34 kilometers on a scale in which the MIlky Way Galaxy was the size of a marble(about 1 cm).
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True or false: Scientific study can always be categorized as belonging to only one of the three major categories of sciences.
True false question.
It is a false statement that Scientific study can always be categorized as belonging to only one of the three major categories of sciences.
What is a scientific study?A scientific study involves an investigation into issues that has to do a scientific topic. There are three main branches of science which are physics, chemistry and biology. However most of the research in science is interdisciplinary. It involves a synergy between the various fields of science.
Thus, it is a false statement that Scientific study can always be categorized as belonging to only one of the three major categories of sciences.
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Bob used a force of 10N to pull a 50 kg trunk a distance of 5 m in 2 seconds. bob's power is
Answer:
25
Explanation:
a = 18t + 10 m/s2
a baseball is thrown vertically upwards into the air (neglect air resistance) and returns to the starting point. true the initial speed and final speed are equal. true the initial velocity and final velocity are equal false the average speed is zero. true the average acceleration is zero. true the total displacement is zero. true the average velocity is zero.
When the baseball is thrown vertically upwards into the air and returns to the starting point,
The average acceleration is not zero
The Initial and final speed are equal
The initial and final velocities are equal
The average speed is not zero
The total displacement is zero
The average velocity is zero.
Define speed vs VelocitySpeed is the temporal speed at which an object moves along a path while velocity is the speed and direction of movement of an object. The mathematical calculation of speed is relatively simple, calculating the average speed of an object by dividing the distance traveled by the time it takes the object to travel the distance. Velocity, on the other hand, is mathematically more complicated and can be calculated in different ways, depending on the available information about the movement of the object. In its simplest form, the average velocity is calculated by dividing the change in position by the change over time.
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one way to monitor global warming is to measure the average temperature of the ocean. researchers are doing this by measuring the time it takes sound pulses to travel underwater over large distances. at a depth of 1000 m, where ocean temperatures hold steady near 4∘c, the average sound speed is 1480m/s. it's known from laboratory measurements that the sound speed increases 4.0m/s for every 1.0∘c increase in temperature. in one experiment, where sounds generated near california are detected in the south pacific, the sound waves travel 7700 km .
The smallest change in average temperature that can be measured is 0.0475°C
CalculationAverage sound speed in deep sea = v=1480m/s
from California to south pacific, sound waves travel 7.7 x [tex]10^{6}[/tex] m distance
smallest time change detected = 1s
The time required for the sound wave to travel the given distance without any change in temperature can be calculated as
t =x/v
=7.7 x [tex]10^{6}[/tex] / 1480
=5202 s
The new time required for the waves,
t1 = t -[tex]\delta t[/tex] =5202-1 =5201s
Now we have to calculate the new sound speed.
v1 = x/t1 = [tex]\frac{7.7 *10^6}{5202}[/tex] =1480.19 m/s
so change in the speed of sound
[tex]\delta v = v1 - v[/tex]
= 1480.19 - 1480 = 0.19 m/s
Then it is given that
[tex]\delta v[/tex] = (4 m/s/°C) [tex]\delta T[/tex](°C)
Formulating,
0.19 m/s = (4 m/s/°C) [tex]\delta T[/tex](°C)
[tex]\delta T[/tex] = 0.19/4
=0.0475°C
Thus, the smallest change in temperature is 0.0475°C
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