Without a figure, it's difficult to provide a specific answer to this question. However, we can provide some general information about using spring scales to weigh objects.
When using two spring scales to weigh an object, it's important to make sure that they are both calibrated and that they are used correctly. Ideally, the scales should be placed at right angles to each other so that the readings are not affected by any sideways forces.
The object being weighed should also be suspended so that it hangs freely, without touching any other objects or the scales themselves.
Assuming that the scales are calibrated and used correctly, the reading on each scale will represent the force exerted by the object in that direction.
For example, if the object is suspended from two scales placed at right angles to each other, the reading on each scale will represent the force exerted by the object in that direction. The total weight of the object can then be calculated using the Pythagorean theorem:
W = sqrt(F1^2 + F2^2)
where W is the weight of the object and F1 and F2 are the forces measured by the two scales.
In this case, since we know the weight of the fish (16 N), we could use the Pythagorean theorem to calculate the readings on the two spring scales.
Learn more about weight here:brainly.com/question/10069252
#SPJ11
an airplane flies 1,592 miles east from arizona to georgia in 3.68 hours. what is the average velocity of the airplane
Answer: Around 433 miles
Explanation:
The speed of light in water is 230Mm/s. Suppose an electron is moving through water at 250 Mm/s . Does that violate the principle of relativity? Explain.
It does not violate the principle of relativity because the speed of the electron in water can explained as its relative speed with water.
What is principle of relativity?
The principle of relativity states that there is no physical way to differentiate between a body moving at a constant speed and an immobile body.
If the speed of light in water is 230Mm/s and an electron is moving through water at 250 Mm/s, it does not violate the principle of relativity because the speed of the electron in water can explained as its relative speed with water.
Learn more about principle of relativity here: https://brainly.com/question/1419696
#SPJ1
A scientist measures the light from a distant star
at 525 nm. The constant for Wien's
displacement law is 2.9 x 10-3 m K. What is the
approximate temperature of the star in Kelvins?
A) 1500 K
B) 180,000 K
C) 1.5 K
D) 5500 K
The approximate temperature of the star as determined is D) 5500 K.
The Wien's displacement law relates the maximum wavelength of a body to its absolute temperature. Wien's displacement law states that:
λ = \(\frac{b}{T}\)
where λ is the maximum wavelength of the body, b is the constant of proportionality and T is the absolute temperature.
Thus from the given question, λ = 525 nm (525 x \(10^{-9}\)), and b = 2.9 x \(10^{-3}\) mK.
So that,
525 x \(10^{-9}\) = \(\frac{2.9*10^{-3} }{T}\)
Make T the subject of the formula to have;
T = \(\frac{2.9*10^{-3} }{525*10^{-9} }\)
= 5523.81
T = 5523.81 K
T ≅ 5500.00 K
The approximate temperature of the star in Kelvin is 5500 K.
For more clarifications, kindly visit: https://brainly.com/question/20038918
How many millimeters of water can dissolve 5g of lead nitrate
The solubility of lead nitrate is 52 grams per 100 milliliters of water at 0°C. Since the question does not specify the temperature, we will assume it is 0°C.To calculate the number of millimeters of water required to dissolve 5 g of lead nitrate,
we must first calculate the number of milliliters of water required to dissolve 5 g of lead nitrate.52 grams of lead nitrate can dissolve in 100 milliliters of water. So,5 g of lead nitrate can dissolve in x milliliters of water.= (5 g / 52 g) × 100 mL= 9.6 mLTherefore, 5 g of lead nitrate can dissolve in 9.6 mL of water. However, the question is asking for the number of millimeters of water, not milliliters. Since 1 milliliter of water weighs 1 gram,9.6 milliliters of water will weigh 9.6 grams.Thus, 5 g of lead nitrate can dissolve in 9.6 millimeters of water.
main answer:5 g of lead nitrate can dissolve in 9.6 millimeters of water. :52 grams of lead nitrate can dissolve in 100 milliliters of water. So, 5 g of lead nitrate can dissolve in x milliliters of water.= (5 g / 52 g) × 100 mL= 9.6 mLTherefore, 5 g of lead nitrate can dissolve in 9.6 mL of water. However, the question is asking for the number of millimeters of water, not milliliters. Since 1 milliliter of water weighs 1 gram,9.6 milliliters of water will weigh 9.6 grams.Thus, 5 g of lead nitrate can dissolve in 9.6 millimeters of water.
To know more about temperature visit;
https://brainly.com/question/30672210
#SPJ11
is the Matter is made up of motionless particles.
Answer:
All matter is made up of atoms.
If earth experienced an iron shortage, where could astronomers direct cosmic mining equipment to find more?
a.
the cores of the other terrestrial planets
b.
the rings of saturn and uranus
c.
the surface of the martian moons
d.
the atmosphere of jupiter
More iron could be found from the cores of the other terrestrial planets. Option A
What is iron?Iron is one of the elements that could be found on earth. This element is present in abundant amounts in the earth's core and ranks as the fourth most abundant element in the core of the earth.
The earth has a lot more deposit of iron in it. We know that earth lies at the center of the solar system for the sole reason that it is habitable. No other planet in the solar system is habitable though efforts are underway to make the other planets equally habitable.
Iron can also be found in the cores of other terrestrial planets but the amounts may be less than the amount of iron that is found on earth. As such, If earth experienced an iron shortage, astronomers could direct cosmic mining equipment to the cores of the other terrestrial planets find more.
Learn more about iron:https://brainly.com/question/18500540
#SPJ1
Classify the statements as correct or incorrect.
A. A thermometer measures the average kinetic energy of a substance.
B. Convection occurs only in liquids and gases.
C. Heat is a form of energy.
D. All substances radiate heat.
E. Heat flows from a colder substance to a hotter substance.
F. Our body temperature is always equal to the temperature around us.
Correct or incorrect
Answer:
A. True
B. ?
C. True
D. False
E. False It is complete opposite
F. ?
Do ocean currents move cold water from the tropics to the poles where the water warms?
Answer: Large-scale surface ocean currents are driven by global wind systems that are fueled by energy from the sun. These currents transfer heat from the tropics to the polar regions, influencing local and global climate.
Explanation:
I hope this helped you some!
No. That would be silly. The water in the tropics is the warmest, since the sun is most direct there.
Any ocean current that takes water away from the tropics moves the water to cooler places, where the water cools off. ESPECIALLY the poles, home of the coldest water on Earth. ICE even !
An object has a mass of 785g and a volume of 15cm cubed what is its density
Answer:
we have ,
mass(m)=785g
volume (v)= 15 cm^3
now , density(d)= m/ v
=785/15
=52.33g/cm^3... is anwer
A toy doll and a toy robot are standing on a frictionless surface facing each other. The doll has a mass of 0.2 kg, and the robot has a mass of 0.5 kg. The robot pushes on the doll with a force of 1 N. The magnitude of the acceleration of the robot is
Answer:
1.43m/s²Explanation:
According to newtons second law.
F = mass * acceleration
If the doll has a mass of 0.2 kg, and the robot has a mass of 0.5 kg, the resulting mass will be 0.7kg
Force applied = 1N
acceleration = Force/mass
Substitute the values and get acceleration
acceleration = 1/0.7
acceleration = 1.43m/s²
Hence the magnitude of the acceleration of the robot is 1.43m/s²
You take a picture of a rainbow with an infrared camera, and your friend takes a picture at the same time with visible light.
Part A:Is the height of the rainbow in the infrared picture greater than, less than, or the same as the height of the rainbow in the visible-light picture?
Part B:Choose the best explanation from among the following:
The height will be less because infrared light is below the visible spectrum.
A rainbow is the same whether seen in visible light or infrared; therefore the height is the same.
The height will be greater because the top of a rainbow is red, and so infrared light would be even higher.
You take a picture of a rainbow with an infrared camera, and your friend takes a picture at the same time with visible light.
Part A: The height of the rainbow in the infrared picture would be the same as the height of the rainbow in the visible-light picture.
Part B: The best explanation is "A rainbow is the same whether seen in visible light or infrared; therefore the height is the same."
Part A: Infrared light and visible light are both part of the electromagnetic spectrum, and they interact with water droplets in the same way to form a rainbow. Therefore, the height of the rainbow, which is determined by the angle of dispersion and reflection, would be the same in both the infrared and visible-light pictures.
Part B:
The height of a rainbow is determined by the angle at which light is dispersed and reflected by water droplets. This angle remains the same regardless of the specific range of the electromagnetic spectrum being observed, be it visible light or infrared light.
While the top of a rainbow appears red in visible light, it is important to note that infrared light is also present in the upper part of the rainbow, but it is not visible to the human eye. Therefore, the height of the rainbow would not be greater in the infrared picture solely because infrared light is "higher" than the visible spectrum.
To know more about visible light here
https://brainly.com/question/15093941
#SPJ4
80 POINTS, BRAINLIEST, AND QUESTION IS MULTIPLE CHOICE!!! (please answer quickly)
question:
If all matter has a gravitational force, why don’t two tennis balls on the ground move towards each other on their own?
A. The force of gravity from the tennis balls is too small.
B.The tennis balls are outside of each other’s gravity field.
C.The tennis balls are too small to produce any gravity.
D.There is too much friction between the balls and the ground
(the picture is just of the question)
Answer:
Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. So as two objects are separated from each other, the force of gravitational attraction between them also decreases.
When dealing with the force of gravity between two objects, there are only two things that are important – mass, and distance. The force of gravity depends directly upon the masses of the two objects, and inversely on the square of the distance between them.
Explanation:
I could be wrong but I would say B :)
Have a good day!
answer:
i believe the answer is d
explanation:
here's why;
c. is incorrect because everything has a gravitational force.
a. is also incorrect because gravity is what holds the tennis ball down and keeps it on the ground.
i don't really know how to explain why b. is wrong, but d. is the correct answer because the force of friction opposes the motion of an object, causing moving objects to lose energy and slow down.
good luck :)
i hope this helps
**please let me know if this was incorrect**
have a great day !!
What questions do you still have about supermassive black holes after watching this Ted Talk? Do you feel that you have a deeper understanding of what they are and why they are important, like was asked of you in the third question? Explain and discuss.
After watching the Ted Talk, there were still a few questions that I had about supermassive black holes. Firstly, I wanted to know more about the event horizon and what it exactly entails. Although the speaker briefly touched upon this subject, I would have appreciated a more in-depth explanation. Additionally, I would have liked to know more about the role of supermassive black holes in the universe.
While the speaker did mention that these black holes are responsible for the creation of galaxies, I wanted to know more about how this process works and why it is so important.Despite these questions, I do feel that I have a deeper understanding of supermassive black holes and their importance.From the Ted Talk, I learned that supermassive black holes are some of the largest objects in the universe and are essential for the formation of galaxies. I also learned that these black holes are incredibly powerful and have the ability to affect the trajectory of stars and planets.Overall, I think that the Ted Talk did a great job of explaining supermassive black holes in a way that was easy to understand. While there were still a few questions that I had after watching the video, I feel that I now have a better grasp of what supermassive black holes are and why they are so important.For such more question on supermassive
https://brainly.com/question/16470114
#SPJ8
A No. _____ THHN conductor is required for a 19.7 ampere load if the ambient temperature is 75F and there are nine current-carrying conductors in the raceway.
A No. 12 THHN conductor is required for a 19.7-ampere load if the ambient temperature is 75F and there are nine current-carrying conductors in the raceway.
To determine the size of the THHN conductor required for a 19.7-ampere load, we will need to use the ampacity tables from the National Electric Code (NEC).
The ampacity tables provide the maximum current-carrying capacity of various types and sizes of conductors based on factors such as ambient temperature and the number of current-carrying conductors in the raceway or cable.
Assuming a copper conductor, we can use NEC Table 310.15(B)(16) to find the ampacity of a No. 12 THHN conductor at an ambient temperature of 75F with nine current-carrying conductors. According to the table, the ampacity of a No. 12 THHN conductor with nine current-carrying conductors at 75F is 20 amperes.
Learn more about the THHN conductor at
https://brainly.com/question/31197467
#SPJ4
An object of mass 3 kg is initially at a temperature of 400K. If the specific heat of this object is 478 J/kg * K, and 13 kJ of heat are added to the object, what is its final temperature?
Given,
The mass of an object is m = 3 kg
Initial temperature, T1 = 400 K
The specific heat of this object is c = 478 J/kg.K
The heat is Q = 13 kJ
Let T2 be the final temperature.
The formula is used to calculate the final temperature.
\(\begin{gathered} Q=mc\Delta T \\ 13\text{ kJ=3 }kg\text{ }\times478\text{ J/}kg\cdot K\text{ }\times(T_2-400\text{)} \\ (T_2-400)=\frac{13\times10^3}{3\times478}_{} \\ T_2-400=9.065 \end{gathered}\)Thus, the value of the final temperature is
\(\begin{gathered} T_2=400+9.065 \\ T_2=409.065\text{ K} \end{gathered}\)Therefore, the given answer (a) is correct.
A 0.0214 m diameter coin rolls up a 13.0◦
inclined plane. The coin starts with an initial
angular speed of 45.4 rad/s and rolls in a
straight line without slipping.
How much vertical height does it gain before it stops rolling?
The coin gains a vertical height of 0.182 m before it stops rolling.
What is angular speed?Angular speed is a term used to describe the rate of change of angular movement.
KE = (1/2)Iω² + (1/2)mv²
I is moment of inertia of the coin, ω is angular velocity, m is mass of coin, and v is its linear velocity.
As v = ωr
r is radius of the coin. For a uniform disk, the moment of inertia is given by: I = (1/2)mr²
KE = (1/2)(1/2)mr²ω² + (1/2)mv²
KE = (1/4)mr²ω² + (1/2)mv²
v = ωr
KE = (1/4)mr²(ω²+ 4v²)
KE = (1/4)(0.0214/2)²(45.4² + 4(0)²) = 0.0235 J
As PE = m g h
m g h = KE
mg(h/g) = KE
h = KE/mg
h = 0.0235/(0.0214/2)²(9.81) = 0.182 m
Therefore, coin gains a vertical height of 0.182 m before it stops rolling.
To know more about angular speed, refer
https://brainly.com/question/6860269
#SPJ1
In a museum exhibit, three equal weights are hung with
identical wires. Each wire can support a tension of no
more than 75.0 N without breaking. What is the maximum value
that W can be without breaking any wires?
A 50.0 N
B 25.0 N
C 75.0 N
D 35.0 N
Answer:(B) 25.0 N
Explanation:
This is what makes most since. You are wanting to look at the stress of the first wire. 25 *3 for the amount of balls handing of the string you get 75.0 N which is the max the top wire can hold without breaking! Hope this helps!
If i place a 300 g mass 20cm from the pivot, what mass, in g, will i have to place 30 cm from the pivot so that my torque bar will be balanced?
To balance the torque bar, we can use the equation: torque = force x distance. In this case, the torque on one side of the pivot should be equal to the torque on the other side.
For the first scenario, the torque is calculated as follows:
Torque1 = (300 g) x (20 cm)
To balance the torque bar, we need to find the mass that should be placed 30 cm from the pivot. Let's call it mass2. The torque equation for this scenario will be:
Torque2 = (mass2 g) x (30 cm)
Since the torque on both sides of the pivot should be balanced, we can set up the equation:
Torque1 = Torque2
(300 g) x (20 cm) = (mass2 g) x (30 cm)
To solve for mass2, we can divide both sides of the equation by 30 cm:
(300 g) x (20 cm) / (30 cm) = mass2 g
After simplifying, we find that mass2 is approximately 200 g.
In summary:
You will have to place a mass of approximately 200 g 30 cm from the pivot to balance the torque bar.
By equating the torques on both sides of the pivot, we can determine the mass required. The torque equation for each side of the pivot is set equal to each other, and by solving the equation, we find that the mass needed is approximately 200 g.
Learn more about the torque bar: https://brainly.com/question/28221040
#SPJ11
How can light be both a wave and a particle? What does that mean?
Answer:
Explanation:
Quantum mechanics tells us that light can behave simultaneously as a particle or a wave. However, there has never been an experiment able to capture both natures of light at the same time; the closest we have come is seeing either wave or particle, but always at different times.When UV light hits a metal surface, it causes an emission of electrons. Albert Einstein explained this "photoelectric" effect by proposing that light – thought to only be a wave – is also a stream of particles
Why is light considered a wave and a particle?
Light behaves mainly like a wave but it can also be considered to consist of tiny packages of energy called photons. Photons carry a fixed amount of energy but have no mass. They also found that increasing the intensity of light increased the number of electrons ejected, but not their speed
What are some of the different measurements scientists can compare using graphs
Answer:
Popular graph types include line graphs, bar graphs, pie charts, scatter plots and histograms. Graphs are a great way to visualize data and display statistics. For example, a bar graph or chart is used to display numerical data that is independent of one another.
Graphs are a useful tool for scientists to visualize and compare different measurements. Here are some examples of measurements that scientists can compare using graphs: Time-series data, Relationships between variables, Proportions, Distribution of data and Comparing groups.
What is scientist ?Before the establishment of contemporary scientific fields, the responsibilities of "scientists" and their forerunners underwent significant change over time. The social norms, ethical principles, and epistemic virtues that have been associated with scientists—and what has been expected of them—over time have also changed. This is true of scientists of different eras as well as of the natural philosophers, mathematicians, historians, theologians, and engineers who preceded them and contributed to the development of science. Consequently, depending on whatever aspects of contemporary science are seen to be crucial, a wide range of historical personalities might be classified as early scientists.
To know more about Scientist :
https://brainly.com/question/17450573
#SPJ2.
2. John starts up his hoverboard, and glides down a track for 10 seconds. He reaches a top
velocity of 36m/s. What is Bader's average acceleration?
The average acceleration of John is 3.6 m/s.
As we know the acceleration of an object is the rate of change of its velocity concerning the time, it is a vector quantity which means it both has direction and magnitude, the orientation of the object depends on the orientation of the total force acting on the object.
As we are given that the initial velocity, u= 0 ms/s( as it started with rest) and the time taken, t= 10 seconds, the final velocity , v= 36 m/s.
As the formula, we can prefer the calculation of the acceleration of an object, which is one of the equations of the motion
v = u+at
Here a= v-u/t
= 36-0/10
= 3.6 m/s
To know more about acceleration refer to the link https://brainly.com/question/12550364?referrer=searchResults.
#SPJ9
hekpppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What property of matter is most responsible for the fact that sound travels at different speeds through different materials?.
Answer:
density
Explanation:
higher density ===> higher propagation speed
How does the Law of Conservation of Energy explain why ice cubes melt in water?
Answer:
because it is an ice that is why it melt
Un móvil viaja inicialmente con una velocidad de 55 m/s, al cabo de cierto tiempo, su velocidad es de 115 m/s, de repente frena bruscamente con una desaceleración de 14, 500 m/s2. ¿qué distancia recorrerá antes de frenar?
Answer:
Distancia, S = 2.84 metros
Explanation:
Dados los siguientes datos;
Velocidad inicial = 55 m/s
Velocidad final = 115 m/s
Deceleración = 14500 m/s²
Para encontrar qué tan lejos viajaría el automóvil, usaríamos la tercera ecuación de movimiento;
V² = U² + 2aS
115² = 55² + 2*14500*S
13225 = 3025 + 29000S
29000S = 13225 - 3025
29000S = 10200
S = 29000/10200
Distancia, S = 2.84 metros
The particles of a GAS within a closed container will collide with the container walls, exerting a FORCE. The force per unit of AREA is known as what?
Answer:
Pressure
Explanation:
One of the theories propounded by the Kinetic molecular theory, and which also provides an explanation of the several gas laws, is the statement that the gas molecules in a container, travel in straight lines and are in constant collision with themselves and the walls of the container, thus exerting force. This force is the pressure which is defined as the force per unit area.
There is no loss of energy in the collisions involving the gas molecules and that is why their movement can be described as elastic. The descriptions of the behavior of gas molecules in the Kinetic Molecular Theory, give rise to Charles law, Boyle's Law, Avogadro's Laws, Dalton's Law, and Amonton's Law.
Answer:
The pressure
Explanation:
Molecules of gases are constantly in motion, colliding with the walls of their container. This constant collision impacts force on the walls of the container, which depends on the speed with which the molecules are moving. The speed with which these molecules travel depends on the average kinetic energy of the molecules, which is proportional to the temperature.
This force when exerted per unit area is the pressure the gases exert on the walls of the container.
what is your centripetal acceleration when you run at 11 m/s around the curve of an olympic track, which has a radius of 36.5 m?
0.30 m/s2
1.2 m/s2
3.3 m/s2
2.4 m/s2
The centripetal acceleration of the person running around the Olympic track will be 3.3m/s².
When the person is running on a circular Olympic track of curve 36.5m with a speed of 11m/s, the person will have some centripetal acceleration equal to a,
Now generally the centripetal acceleration of any body running in a circular manner is given by the relation,
a = v²/R
Where,
v is the speed at which the person is running and R is the radius of the circular track.
Now, putting the value used to find the centripetal acceleration of the person running on the Olympic track.
a = (11)²/36.5
a = 3.3m/s²
So, the centripetal acceleration of the person is 3.3m/s².
To know more about centripetal acceleration, visit,
https://brainly.com/question/22103069
#SPJ4
Slim Jim, continually maintaining his svelte body, lifts a 70 kg barbell 1.4m above the grounda) How much energy did the barbell have when it was on the ground?b) How much energy does it have after being lifted 1.4m? What kind of energy does it have afterbeing lifted? Where did it come from?c) How much work did Jim do to the lift the object?dIf he lifted it in 1.5s how much power did he use?
Given,
The mass of the barbell, m=70 kg
The height to which Slim Jim lifts the barbell, h=1.4 m
a)
When the barbell was on the ground, it will have zero kinetic energy as it has no velocity. And if assume the height of ground as zero meters, then its potential energy is also zero.
Thus when the barbell was on the ground, its energy was zero joules.
b)
The energy of the barbell when it is at a height of h is given by,
\(E=\text{mgh}\)Where g is the acceleration due to gravity.
On substituting the known values,
\(\begin{gathered} E=70\times9.8\times1.4 \\ =960.4\text{ J} \end{gathered}\)Thus the energy that the barbell has after being lifted 1.4 m is 960.4 J
This energy is the energy stored in the barbell due to its position. Thus the energy stored in the barbell is the potential energy.
Slim Jim has to do some work to lift the barbell to the given height. This work done will be stored in the barbell in the form of potential energy. That is, the energy of the barbell is supplied to it from Slim Jim through the work.
c)
All the work done by Jim will be stored in the barbell in the form of potential energy. Thus, the work done by Jim is equal to the potential energy of the barbel.
Therefore, the work done by Jim is 960.4 J
d)
Given,
The time interval, t=1.5 s
The power is given by,
\(P=\frac{W}{t}\)Where W is the work done by Jim.
On substituting the known values,
\(\begin{gathered} P=\frac{960.4}{1.5} \\ =640.27\text{ W} \end{gathered}\)Thus the power used by Jim is 640.27 W
PLEASE HELP!!
5. A 700 kg race car travels
around the track at 65 m/s. The track has a radius of 75 m.
a. What is the centripetal acceleration?
b. What is the centripetal force?
c. Is the net force on the car less than, equal to, or greater than the centripetal force? Why?
Hi there!
a.
The equation for centripetal acceleration is as follows:
\(\large\boxed{a_c = \frac{v^2}{r}}}\)
Plug in the given values to solve:
\(\large\boxed{a_c = \frac{(65)^2}{75} = 56.33 m/s^2}\)
b.
According to Newton's Second Law:
\(\large\boxed{\Sigma F = ma}}\)
The acceleration is v²/r, so the net force is:
\(\large\boxed{\Sigma F = m(\frac{v^2}{r})}}\)
Multiply by the given mass:
\(\large\boxed{\Sigma F = 700(56.33) = 39433.33 N}}\)
c.
There is NO net force in the vertical direction since the object is NOT accelerating in the vertical direction (normal force and weight cancel).
Thus, the ONLY net force experienced by the object is in the horizontal direction and is EQUAL to the centripetal force.
Salmon often jump waterfalls to reach their
breeding grounds.
Starting downstream, 3.02 m away from a
waterfall 0.258 m in height, at what minimum
speed must a salmon jumping at an angle of
36.2° leave the water to continue upstream?
The acceleration due to gravity is 9.81 m/s².
Answer in units of m/s.
Answer:
easeaseaseas
Explanation:
Answer:
5.93 m/s (2 d.p.)
Explanation:
When a body is projected through the air with initial speed u, at an angle of θ to the horizontal, it will move along a curved path.
Therefore, trigonometry can be used to resolve the body's initial velocity into its vertical and horizontal components:
\(\textsf{Horizontal component of $u= u \cos \theta$}\)\(\textsf{Vertical component of $u= u \sin\theta$}\)As the projectile is modeled as moving only under the influence of gravity, the only acceleration the projectile will experience will be acceleration due to gravity.
Constant Acceleration Equations (SUVAT)
\(\boxed{\begin{array}{c}\begin{aligned}v&=u+at\\\\s&=ut+\dfrac{1}{2}at^2\\\\ s&=\left(\dfrac{u+v}{2}\right)t\\\\v^2&=u^2+2as\\\\s&=vt-\dfrac{1}{2}at^2\end{aligned}\end{array}} \quad \boxed{\begin{minipage}{4.6 cm}$s$ = displacement in m\\\\$u$ = initial velocity in ms$^{-1}$\\\\$v$ = final velocity in ms$^{-1}$\\\\$a$ = acceleration in ms$^{-2}$\\\\$t$ = time in s (seconds)\end{minipage}}\)
When using SUVAT, assume the object is modeled as a particle and that acceleration is constant.
If the salmon jumps at an angle of 36.2° then:
\(\textsf{Horizontal component of $u= u \cos 36.2^{\circ}$}\)\(\textsf{Vertical component of $u= u \sin36.2^{\circ}$}\)Resolving horizontallyThe horizontal component of velocity is constant, as there is no acceleration horizontally.
Resolving horizontally, taking → as positive:
\(s=3.02 \quad u=u \cos 36.2^{\circ} \quad v=u \cos 36.2^{\circ} \quad a=0\)
\(\begin{aligned}\textsf{Using} \quad s & =ut+\dfrac{1}{2}at^2\\\\3.02 & = (u \cos 36.2^{\circ})t+\dfrac{1}{2}(0)t^2\\3.02 & = (u \cos 36.2^{\circ})t\\\implies t&=\dfrac{3.02}{u \cos 36.2^{\circ}}\end{aligned}\)
Resolving verticallyAcceleration due to gravity = 9.81 ms⁻²
Resolving vertically, taking ↑ as positive and using the found expression for t:
\(s=0.258 \quad u=u \sin 36.2^{\circ} \quad a=-9.81 \quad t=\dfrac{3.02}{u \cos 36.2^{\circ}}\)
\(\begin{aligned}\textsf{Using} \quad s & =ut+\dfrac{1}{2}at^2\\\\0.258 & = (u \sin 36.2^{\circ})\left(\dfrac{3.02}{u \cos 36.2^{\circ}}\right)+\dfrac{1}{2}(-9.81)\left(\dfrac{3.02}{u \cos 36.2^{\circ}}\right)^2\\0.258&=3.02 \tan36.2^{\circ}-4.905\left(\dfrac{9.1204}{u^2 \cos^2 36.2^{\circ}}\right)\\0.258-3.02 \tan36.2^{\circ}&=-\dfrac{44.735562}{u^2 \cos^2 36.2^{\circ}}\\u^2&=-\dfrac{44.735562}{(0.258-3.02 \tan36.2^{\circ})(\cos^2 36.2^{\circ})}\\u^2&=35.18849443\\ u&=5.931989079\end{aligned}\)
Therefore, the minimum speed at which the salmon should leave the water is 5.93 m/s (2 d.p.).