Two blocks are placed at the ends of a horizontal massless board, as in the drawing. The board is kept from rotating and rests on a support that serves as an axis of rotation. The block on the right has a mass of 5.8 kg. Determine the magnitude of the angular acceleration when the system is allowed to rotate.

Answer:

Radiation

Explanation:

Radiation is the transfer of energy that doesn't require the movement of matter, so the energy is transferred by electromagnetic waves, therefore, the heat travels from the sun to earth through the process of radiation.

The two gases that could be components of water are indeed hydrogen and oxygen.

Evidence to support this claim:

1. The chemical formula for water is H2O, which means that it is composed of two hydrogen atoms and one oxygen atom.

2. The table of elements shows that hydrogen (H) and oxygen (O) are both elements that exist in nature.

3. The atomic mass of hydrogen (1.008) and oxygen (15.999) matches the molecular mass of water (18.015).

4. Water is produced when hydrogen gas (H2) is burned in the presence of oxygen gas (O2), according to the following equation: 2H2 + O2 → 2H2O.

Overall, the evidence supports the conclusion that hydrogen and oxygen are the two gases that could be components of water.

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The difference between an atom's mass number (A) and atomic number (Z) is equal to the number of neutrons.

1) H – Hydrogen - 1 proton, 1 electron, 0 neutrons

2) He – Helium - 2 protons, 2 electrons, 2 neutrons

3) Li – Lithium - 3 protons, 3 electrons, 4 neutrons

4) Be – Beryllium - 4 protons, 4 electrons, 5 neutrons

5) B – Boron - 5 protons, 5 electrons, 6 neutrons

6) C – Carbon - 6 protons, 6 electrons, 6 neutrons

7) N – Nitrogen - 7 protons, 7 electrons, 8 neutrons

8) O – Oxygen - 8 protons, 8 electrons, 8 neutrons

9) F – Fluorine - 9 protons, 9 electrons, 10 neutrons

10)Ne – Neon - 10 protons, 10 electrons, 10 neutrons

11) Na – Sodium - 11 protons, 11 electrons, 12 neutrons

12) Mg – Magnesium - 12 protons, 12 electrons, 12 neutrons

13) Al – Aluminium - 13 protons, 13 electrons, 14 neutrons

14) Si – Silicon - 14 protons, 14 electrons, 14 neutrons

15) P – Phosphorus - 15 protons, 15 electrons, 17 neutrons

16) S – Sulphur - 16 protons, 16 electrons, 16 neutrons

17) Cl – Chlorine - 17 protons, 17 electrons, 18 neutrons

18) Ar – Argon - 18 protons, 18 electrons, 22 neutrons

19) K – Potassium - 19 protons, 19 electrons, 20 neutrons

20) Ca – Calcium - 20 protons, 20 electrons, 28 neutrons

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because it uses a systematic method of asking and answering problems, and it attempts to develop solution to psychological problems.

Answer:

it uses a systematic method of asking and answering problems,

Explanation:

The pulleys can be attached in such a way that the force required to lift the object will be less, and the direction of the pulley can be shifted systematically.

In the body, force is the result of either a push or a pull. The three main categories of forces are friction, nuclear, and gravitational. For instance, when a hand strikes a wall, the hand puts force on the wall and the wall also exerts a force on the hand. Newton was given a variety of laws to help him understand force.

We can move objects much more easily because of simple machinery called pulleys that can shift the direction of the force. When we employ many pulleys together, they also boost mechanical advantage. By using this method, less force is needed to raise an object.

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The electric field of magnitude 16 N/C will be at a distance of 6.0 meters from the charged object.

The magnitude of the electric field due to a point charge object follows the inverse square law, which states that the magnitude of the electric field is inversely proportional to the square of the distance from the charged object. Mathematically, this is expressed as:

\(E = k*q/r^2\)

where E is the electric field, k is Coulomb's constant (\(k = 9 x 10^9 N*m^2/C^2\)), q is the charge of the object, and r is the distance from the object.

We can use this formula to find the distance at which the electric field has a magnitude of 16 N/C. Let's call this distance x:

16 = \(k*q/x^2\)

We can rearrange this equation to solve for x:

x = \(\sqrt(k*q/16)\)

To find q, we need another piece of information. We know that the electric field has a magnitude of 9 N/C at a distance of 4.0 m. Using the same formula as before, we can solve for q:

9 = \(k*q/4^2\)

q = \(9*4^2/k\)

Now we can substitute this value for q into the equation for x:

x =\(\sqrt(k*(9*4^2/k)/16)\)

x =\(\sqrt(9*4^2/16)\)

x = \(\sqrt(36)\)

x = 6.0 meters

Therefore, the electric field of magnitude 16 N/C will be at a distance of 6.0 meters from the charged object.

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Answer:

a. 13.96 m/s in the +x direction

b. -1.76 m/s that is 1.76 m/s in the -x direction

Explanation:

(a) Calculate the magnitude of the velocity of the puck after a force of 37.0 N directed to the right has been applied for 0.050 s.

Since Impulse, I = Ft = m(v₂ - v₁) where F = force applied = + 37.0 N(positive since it is applied to the right), t = duration of applied force = 0.050 s, m = mass of hockey puck = 0.160 kg, v₁ = initial velocity of hockey puck =  + 2,40 m/s (positive since it is moving to the right) and v₂ = final velocity of hockey puck

So, making v₂ subject of the formula, we have

v₂ = v₁ + Ft/m

substituting the values of the variables into the equation, we have

v₂ = v₁ + Ft/m

v₂ = 2.40 m/s + 37.0 N × 0.050 s/0.160 kg

v₂ = 2.40 m/s + 1.85 Ns/0.160 kg

v₂ = 2.40 m/s + 11.56 m/s

v₂ = 13.96 m/s

(b) If instead, a force of 13.3 N directed to the left is applied from t = 0 to t =0.050 s, what is the final velocity of the puck?

Since Impulse, I = Ft = m(v₂ - v₁) where F = force applied = - 13.3 N(positive since it is applied to the right), t = duration of applied force = 0.050 s, m = mass of hockey puck = 0.160 kg, v₁ = initial velocity of hockey puck =  + 2,40 m/s (positive since it is moving to the right) and v₂ = final velocity of hockey puck

So, making v₂ subject of the formula, we have

v₂ = v₁ + Ft/m

substituting the values of the variables into the equation, we have

v₂ = v₁ + Ft/m

v₂ = 2.40 m/s + (-13.3 N) × 0.050 s/0.160 kg

v₂ = 2.40 m/s - 0.665 Ns/0.160 kg

v₂ = 2.40 m/s - 4.156 m/s

v₂ = -1.756 m/s

v₂ ≅ -1.76 m/s

(a). The velocity of the puck is 13.96 m/s in the +x direction

(b). The final velocity of the puck is -1.76 m/s which is 1.76 m/s in the -x direction

The velocity of the object is defined as the movement of the object in a particular direction with respect to time.

(a) Calculate the magnitude of the velocity of the puck after a force of 37.0 N directed to the right has been applied for 0.050 s.

It is given that

Impulse, I = Ft = m(v₂ - v₁)

where F = force applied = + 37.0 N(positive since it is applied to the right),

t = duration of applied force = 0.050 s,

m = mass of hockey puck = 0.160 kg,

v₁ = initial velocity of hockey puck =  + 2,40 m/s (positive since it is moving to the right)  

v₂ = final velocity of a hockey puck

So, making v₂ subject of the formula, we have

\(V_2=v_1+\dfrac{Ft}{m}\)

substituting the values of the variables into the equation, we have

\(v_2=2.40+\dfrac{37\times 0.050}{0.160}\)

\(v_2=2.40+11.56\)

\(v_2=13.96\ \dfrac{m}{s}\)

(b) If instead, a force of 13.3 N directed to the left is applied from t = 0 to t =0.050 s, what is the final velocity of the puck?

Since Impulse, I = Ft = m(v₂ - v₁)

where F = force applied = - 13.3 N(positive since it is applied to the right),

t = duration of applied force = 0.050 s,

m = mass of hockey puck = 0.160 kg,

v₁ = initial velocity of hockey puck =  + 2,40 m/s (positive since it is moving to the right)  

v₂ = final velocity of a hockey puck

So, making v₂ subject of the formula, we have

\(v_2=v_1+\dfrac{Ft}{m}\)

substituting the values of the variables into the equation, we have

\(v_2=2.40+\dfrac{-13.3\times 0.050}{0.160}\)

\(v_2=2.40-4.156\)

\(v+2=-1.76\ \frac{m}{s}\)

Thus

(a). The velocity of the puck is 13.96 m/s in the +x direction

(b). The final velocity of the puck is -1.76 m/s which is 1.76 m/s in the -x direction

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Answer:

Total distance = 700 m

Displacement = 500 m

Explanation:

Notice that Jed travelled a total of 3 x 100 m = 300 m in the North direction, and 300 m + 100 m = 400 m in the East direction. Therefore the total distance he travelled is:  300 + 400 = 700 m.

But the actual displacement is given by the Pythagorean theorem as the hypotenuse of a right angle triangle of legs 300 m and 400 m:

displacement = \(\sqrt{300^2+400^2} =\sqrt{250000} =500\,m\)

Answer:

the last one

Explanation:

ii took the quiz and it was right... i think

Answer:

Answers 2.( a) . (i)Total potential difference provided by the four cell = 4x 1.5 Volts = 6.0 Volts (ii)The component of X is a variable resistor .

Explanation:

hope it helps

The total potential difference provided by the four cells in the circuit each of 1.5volts is 6 volts.

The potential difference between two points in a circuit is the difference in the amount of energy that charge carriers have.

Volts are measured as follows: Potential difference is also known as voltage and is measured in volts (V).

The external work required to move a charge from one location to another in an electric field is known as the electric potential difference, also known as voltage.

When electrical cells are connected in series, such as in a battery, the battery's potential difference is the sum of the potential differences of each cell. As a result, the battery's potential difference is the sum of their potential differences.

It is given that:

The voltage of each cell = 1.5 volts.

So, the potential difference = 4 x 1.5

Potential difference = 6 volts.

Thus, the total potential difference is 6 volts.

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The hiker travelled 4.02 km North/South and 4.74 km East/West during her hike.

This question involves vector addition, the resolution of vectors, the use of bearings, and trigonometry in the calculation of the hiker's movement.

This may appear to be a difficult problem, but with some visual aid and the proper use of mathematical formulas, the issue can be addressed correctly.

Resolution of VectorThe resolution of a vector is the process of dividing it into two or more components.

The angle between the resultant and the given vector is equal to the inverse tangent of the two rectangular components.

Angles will always be expressed in degrees in the solution.

The sine, cosine, and tangent functions in trigonometry are denoted by sin, cos, and tan.

The tangent function can be calculated using the sine and cosine functions as tan x = sin x/cos x. Also, in right-angled triangles, Pythagoras’ theorem is used to find the hypotenuse or one of the legs.

Distance Travelled North/SouthThe hiker traveled North for the first part of the hike and South for the second.

The angles that the hiker traveled in the first part and second parts are 53 degrees and 17 degrees, respectively.

The angle between the two is (180 - 53 - 17) = 110 degrees.

The angle between the resultant and the Northern direction is 110 - 53 = 57 degrees.

Using sine and cosine, we can calculate the north/south distance traveled to be 5 sin 57 = 4.02 km, and the east/west distance to be 5 cos 57 = 2.93 km.

Distance Travelled East/WestThe hiker walked East for the second part of the hike.

To calculate the distance travelled East/West, we must first calculate the component of the first part that was East/West.

The angle between the vector and the Eastern direction is 90 - 53 = 37 degrees.

Using sine and cosine, we can calculate that the distance travelled East/West for the first part of the hike is 5 cos 37 = 3.88 km.

To determine the net distance travelled East/West, we must combine this component with the distance travelled East/West in the second part of the hike.

The angle between the second vector and the Eastern direction is 17 degrees.

Using sine and cosine, we can calculate the distance traveled East/West to be 3 sin 17 = 0.86 km.

The net distance traveled East/West is 3.88 + 0.86 = 4.74 km.

Therefore, the hiker travelled 4.02 km North/South and 4.74 km East/West during her hike.

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The weight applied at the center of mass G and the pin at A there will only be a vertical force and at B there will a force perpendicular to the direction that the axis.

The 4-lb uniform rod AB is attached to collars of negligible mass that slide without friction along the fixed rods shown. Rod AB is at rest in the position u = 258 when a horizontal force P is applied to collar A causing it to start moving to the left. Draw the FBD and KD for the rod. the following steps can be taken:

1. Draw a diagram of the system, including the fixed rods, collars, and the uniform rod AB.

2. Identify the forces acting on the system. There are two forces acting on the uniform rod AB: the horizontal force P applied to collar A, and the weight of the rod, which acts downwards.

3. Draw a free-body diagram (FBD) of the uniform rod AB, showing the forces acting on the rod.

4. Draw a kinetic diagram (KD) of the uniform rod AB, showing the velocity and acceleration of the rod. Since the rod is at rest initially, its velocity is zero, and its acceleration is determined by the net force acting on it, which is P.

5. Use Newton's second law to determine the acceleration of the rod, which is equal to the net force acting on it divided by its mass.

6. Use the acceleration of the rod to determine the velocity and position of the rod at any given time.

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Answer:

When it comes to research questions, sociologists are best equipped to answer empirical questions. —those that can be answered by real experience in the real world—as opposed to ethical questions. —questions about which people have moral opinions and that may not be answerable in reference to the real world.

Explanation:

Answer:

So the answer is C: 2 Ω.

Explanation:

The equivalent resistance of a parallel circuit is given by the formula:

1/R_equiv = 1/R1 + 1/R2 + ... + 1/Rn

In this case, there are 5 resistors each with a resistance of 10 ohms, so:

1/R_equiv = 1/10 + 1/10 + 1/10 + 1/10 + 1/10 = 5/10 = 0.5

And the equivalent resistance is:

R_equiv = 1 / 0.5 = 2 ohms

So the answer is C: 2 Ω.

The scientific study of physics focuses on the underlying concepts that underpin the laws of nature. It investigates how matter, energy, space, and time behave and interact. Physics' fundamental goal is to comprehend the underlying laws and forces that create our universe.

Physics has developed theories and rules to explain a wide variety of events, from the motion of celestial bodies to the behaviour of subatomic particles, via meticulous observation, investigation, and mathematical analysis.

These theories offer a framework for comprehending and forecasting the behaviour of physical systems, such as Newton's laws of motion and Einstein's theory of relativity.

From the tiniest particles to the biggest cosmic structures, physics has enhanced our understanding of the world and sparked a host of technological advances.

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The average velocity of the car is 37.27 km/h.

The given parameters;

The average velocity of the car is calculated as follows;

\(average \ velocity = \frac{Total \ displacement}{Total \ time}\)

The total displacement of the car is calculated as follows;

\(d = \sqrt{x^2 + y^2} \\\\d = \sqrt{100^2 \ + \ 50^2} \\\\d = 111.803 \ km\)

The average velocity of the car is calculated as follows;

\(v = \frac{111.803}{3} \\\\v = 37.27 \ km/h\)

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Option C. The heat absorbed or lost by a substance while it's changing state  correctly describes latent heat

Latent heat is the heat absorbed or lost by a substance while it is changing state.

The latent heat is a type of heat that is transferred during phase change, i.e., while a substance undergoes a change of state.

For example, when ice melts into liquid water, or when liquid water evaporates into water vapor, heat is absorbed from the surroundings.

Latent heat is not associated with a temperature change; rather, it's associated with a change of state.

For instance, the temperature of water remains at 100°C while boiling.

When water is boiling, the latent heat of vaporization is absorbed and utilized to break the hydrogen bonds holding water molecules together to change water from the liquid phase to the gaseous phase.

When the water is boiling, adding more heat won't increase the water's temperature, instead, the extra heat will be absorbed to change the phase of water molecules.

Therefore, the correct answer to the given question is option C: The heat absorbed or lost by a substance while it is changing state.

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Answer:

Warm Room

Explanation:

Sound, like any wave, is a transfer of energy from one particle to another.

As temperature rises, each particle will have more energy; they will collide into other particles more often.

As the frequency of collisions increase, the speed of which the sound wave is transferred increases.

(a) The location of a point where the electric field is zero is at the center of the triangle which is equal to ¹/₆√3a.

(b) The magnitude and direction of the electric field at the top corner due to the two charges at the base is  1.732 kq/a².

The electric field is zero at the center of the equilateral triangle whose magnitude is equal to √3a/6.

E = E₁ + E₂

where;

E = kq/a²[(cos 60i + sin 60j) + (-cos 60i + sin 60j)]

E = kq/a²[2(sin 60j)] = 1.732 kq/a²

Thus, the location of a point where the electric field is zero is at the center of the triangle which is equal to ¹/₆√3a.

The magnitude and direction of the electric field at the top corner due to the two charges at the base is  1.732 kq/a².

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The constant acceleration of the train is 0.33 m/s.

The average velocity can be calculated by using the formula:

velocity = distance/time

For the 1st car, the velocity is calculated as:

v₁ = 8.60 m / 1.80 s = 4.78 m / s

For the second car, velocity can be calculated as:

v₂ = 8.60 m / 1.66 s = 5.34 m / s

Now we can solve for the acceleration using the formula:

v₂² = v₁² + 2 a d

Rewriting in terms of a, we get

a = (v₂² – v₁²) / 2 d

a = (5.34)² – (4.78)² / (2 × 8.6)

a = 0.33 m/s

Therefore, the constant acceleration of the train is 0.33m/s.

what is acceleration explain?

acceleration, fee at which speed modifications with time, in terms of each pace and course. A factor or an object shifting in a directly line is improved if it hastens or slows down. motion on a circle is improved even if the velocity is steady, due to the fact the route is constantly converting

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The disorder that does not appear to describe Greta's possible condition is epilepsy. The correct answer is B.

While epilepsy is a neurological disorder that can cause seizures and other symptoms, it does not typically result in the physical challenges that Greta is experiencing, such as spasticity and the need for a variable-speed tape recorder.

Additionally, epilepsy does not necessarily affect an individual's ability to communicate using finger spelling or impact their hearing or vision. Therefore, while Greta may have epilepsy in addition to her other challenges, it is not directly related to the issues she is experiencing in Mr. Popanopoulous' class.

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Your question seems incomplete, but I suppose the question was:

"Greta is experiencing difficulty in Mr. Popanopoulous' class because she has different needs than many of the other students. Greta must use a variable-speed tape recorder to record the lessons, she often struggles with spasticity, and she frequently uses finger spelling as a method of communication. Which of the following disorders does NOT appear to describe Greta's possible condition?

A) Cerebral palsy

B) Epilepsy

C) Hearing impairment

D) Visual impairment"

Answer:

B

Explanation:

The seasons are measured in how far or close the earth is to the sun.

ANSWER:

212.18 pascals

STEP-BY-STEP EXPLANATION:

Given:

Side: 1.21 m

The area is:

Mass of the box: 31.7 kg

Force due to gravity:

The pressure would be:

The pressure is 212.18 pascals

The maximal potential energy is present at the highest point, and there is no kinetic energy due to the zero ultimate velocity at the lowest point.

The potential energy is due to the virtue of the position and the height. The unit for the potential energy is the joule.

The potential energy is mainly depending upon the height of the object.

When the egg is at the highest position, the height is maximum. Therefore, the potential energy is also maximum.

When the egg lands on the ground at the striking point only the kinetic energy exists the potential energy is zero.

According to the law of conservation of energy, total energy is defined as the sum of kinetic energy and potential energy.

Total energy = kinetic energy+potential energy

Also, the energy can not be created nor destroyed and can be transferred from one form to another form.

Hence, at the highest point potential energy is the maximum and the kinetic energy is zero. because the final velocity is zero.

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At the highest point,  the maximum potential energy is present. But kinetic energy is not present because of zero velocity at the lowest point.

Potential energy is the energy posses by an object due to its position relative to other objects , which it stresses within itself.

Potential energy depends upon the height of the object. its SI unit is joule.

When egg rises to the maximum height from the ground surface, the potential energy is also maximum.

When the egg falls and lands on the ground , the potential energy will be zero. It posses only kinetic energy.

By the law of conservation of energy ,

The energy is neither be created nor be destroyed and cannot be transferred from one form to another.

Therefore, At the highest point the potential energy is  maximum. But kinetic energy is zero.

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Melvina's potential energy is 54,880 Joules.

To calculate Melvina's potential energy, we need to use the formula for gravitational potential energy:

Potential energy = mass × gravitational acceleration × height

Potential energy is a measure of the energy an object possesses due to its position relative to other objects. In this case, Melvina's potential energy is a result of her height above the ground. As she stands on the ledge of the burning building, her potential energy is stored and can be converted into other forms of energy if she were to jump or fall. The potential energy will decrease as she descends, and it will be converted into kinetic energy (energy of motion).

Given that Melvina has a mass of 70 kg and the ledge is 80 m above the ground, we can substitute the values into the formula:

Potential energy = 70 kg × 9.8 m/s² × 80 m

Calculating this, we find:

Potential energy = 54,880 Joules

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Answer:

Speed of the spacecraft right before the collision: \(\displaystyle \sqrt{\frac{2\, G\cdot M_\text{e}}{R\text{e}}}\).

Assumption: the earth is exactly spherical with a uniform density.

Explanation:

This question could be solved using the conservation of energy.

The mechanical energy of this spacecraft is the sum of:

Let \(m\) denote the mass of this spacecraft. At a distance of \(R\) from the center of the earth (with mass \(M_\text{e}\)), the gravitational potential energy (\(\mathrm{GPE}\)) of this spacecraft would be:

\(\displaystyle \text{GPE} = -\frac{G \cdot M_\text{e}\cdot m}{R}\).

Initially, \(R\) (the denominator of this fraction) is infinitely large. Therefore, the initial value of \(\mathrm{GPE}\) will be infinitely close to zero.

On the other hand, the question states that the initial kinetic energy (\(\rm KE\)) of this spacecraft is also zero. Therefore, the initial mechanical energy of this spacecraft would be zero.

Right before the collision, the spacecraft would be very close to the surface of the earth. The distance \(R\) between the spacecraft and the center of the earth would be approximately equal to \(R_\text{e}\), the radius of the earth.

The \(\mathrm{GPE}\) of the spacecraft at that moment would be:

\(\displaystyle \text{GPE} = -\frac{G \cdot M_\text{e}\cdot m}{R_\text{e}}\).

Subtract this value from zero to find the loss in the \(\rm GPE\) of this spacecraft:

\(\begin{aligned}\text{GPE change} &= \text{Initial GPE} - \text{Final GPE} \\ &= 0 - \left(-\frac{G \cdot M_\text{e}\cdot m}{R_\text{e}}\right) = \frac{G \cdot M_\text{e}\cdot m}{R_\text{e}} \end{aligned}\)

Assume that gravitational pull is the only force on the spacecraft. The size of the loss in the \(\rm GPE\) of this spacecraft would be equal to the size of the gain in its \(\rm KE\).

Therefore, right before collision, the \(\rm KE\) of this spacecraft would be:

\(\begin{aligned}& \text{Initial KE} + \text{KE change} \\ &= \text{Initial KE} + (-\text{GPE change}) \\ &= 0 + \frac{G \cdot M_\text{e}\cdot m}{R_\text{e}} \\ &= \frac{G \cdot M_\text{e}\cdot m}{R_\text{e}}\end{aligned}\).

On the other hand, let \(v\) denote the speed of this spacecraft. The following equation that relates \(v\!\) and \(m\) to \(\rm KE\):

\(\displaystyle \text{KE} = \frac{1}{2}\, m \cdot v^2\).

Rearrange this equation to find an equation for \(v\):

\(\displaystyle v = \sqrt{\frac{2\, \text{KE}}{m}}\).

It is already found that right before the collision, \(\displaystyle \text{KE} = \frac{G \cdot M_\text{e}\cdot m}{R_\text{e}}\). Make use of this equation to find \(v\) at that moment:

\(\begin{aligned}v &= \sqrt{\frac{2\, \text{KE}}{m}} \\ &= \sqrt{\frac{2\, G\cdot M_\text{e} \cdot m}{R_\text{e}\cdot m}} = \sqrt{\frac{2\, G\cdot M_\text{e}}{R_\text{e}}}\end{aligned}\).

Answer:  4182 J/kg°C

Explanation: molar heat capacity is J/mole C not J/gC. 4.18 J/gC x (18.0 g / mole) = 75.2 J/moleC

the Speed reached by the bicyclist is given by, v = 26 m/s

There are mainly four types of friction: static friction, sliding friction, rolling friction, and fluid friction. Friction and normal force are directly proportional to the contacting surfaces, and it doesn't depend on the hardness of the contacting surface.

Given that,

Gravitational acceleration = 9.81 m/s²

Mass of bicyclist = 80 kg

Slope(θ) = 5°

Cross-sectional area of bicyclist = 0.35 m²

μ = coefficient of rolling friction = 0.02

t = air temperature = 20 °C

Let ρ be the density of air at 20oC = 1.2041 kg/m3

ρ = 1.2041 kg/m3

We have the balancing equation:

F₁ = F₂ + F₃

where,

F₁ = component of the weight of the bicyclist down the plane,

F₂ = frictional force up the plane, and

F₃ = air drag force up the plane.

Thus, F₃ = F₁ - F₂

sinθ = sin(5°) = 0.087

cosθ = cos(5°) = 0.996

Now we will calculate the forces,

F₁ = m g sinθ = 80 kg x 9.81 m/s2 x 0.087 = 68.227 N

F₁ = 68.227 N

F₂ = μ m g cosθ = 0.02 x 80 kg x 9.81 m/s2 x 0.996 = 15.63 N

F₂ = 15.63 N

Put the values of F1 and F2 in eqn (1) and we get:

F₃ = F1 - F2

F₃ = 68.227 - 15.63

F₃ = 52.597 N

Let v be the speed reached by a bicyclist,

From the general formula of velocity:

V = ((2 xF₃ / (ρ x CD x A))1/2

v = ((2 x F₃ / (ρ x CD x A))1/2

v = ((2 x 120.78 N / (1.2041 kg/m3 x 0.85 x 0.35))1/2 = 25.97 m/s

v = 26 m/s

Therefore, the Speed reached by the bicyclist is given by, v = 26 m/s

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