The longest recorded pass in an NFL game traveled 83 yards in the air from the quarterback to the receiver.
Part A
Assuming that the pass was thrown at the optimal 45 angle, what was the speed at which the ball left the quarterback's hand?

Answer:

Batteries are intended to store chemical energy and then it converts into electricidal energy. So overall, batteries produce energy.

Explanation:

Answer:

 α = 2.13 10⁻⁵ C⁻¹    ,  the closest material is ALUMINUM

Explanation:

The expression for thermal expansion is

          ΔL = α L₀ ΔT

temperatures are

         ΔT = 85 - 10 = 75 ° C

the length of the rod is L₀ = 125 m and L_f = 125.20 m

        ΔL = 125.20 - 125 = 0.20 m

        α = [tex]\frac{1}{L_o} \frac{\Delta L }{\Delta T}[/tex]

        α = [tex]\frac{ 1}{125} \ \frac{0.20 }{75}[/tex]

        α = 2.13 10⁻⁵ C⁻¹

When reviewing the table, the closest material is ALUMINUM

To transition of the satellite from a circular orbit with radius R to an elliptical orbit with rmin = R and rmax = 2R, the velocity v must be increased by a factor of 2.

In a circular orbit, the centripetal force required to keep the satellite in orbit is provided by the gravitational force between the satellite and the Earth.

Fcircular = Fgravity

The centripetal force in a circular orbit can be expressed as:

Fcircular = (mv²) / R

where m is the mass of the satellite, v is the velocity, and R is the radius of the circular orbit.

The gravitational force between the satellite and the Earth can be expressed using Newton's law of universal gravitation:

Fgravity = (G × m × M) / R²

where G is the gravitational constant and M is the mass of the Earth.

Equating the centripetal force and the gravitational force, we get:

(mv²) / R = (G × m × M) / R²

Canceling the mass (m) on both sides of the equation, we have:

v² / R = (G × M) / R²

Rearranging the equation to solve for v, we get:

v = √((G × M) / R)

Now, let's consider the elliptical orbit. The minimum radius (rmin) is R and the maximum radius (rmax) is 2R.

The velocity in the elliptical orbit at rmin can be calculated using the same equation as before:

vmin = √((G × M) / rmin)

Similarly, the velocity in the elliptical orbit at rmax can be calculated:

vmax = √((G × M) / rmax)

Now, we need to find the ratio of vmax to vmin:

vmax / vmin = √((G × M) / rmax) / √((G × M) / rmin)

Simplifying the expression:

vmax / vmin = √(rmin / rmax)

Substituting the given values rmin = R and rmax = 2R:

vmax / vmin = √(R / (2R))

Simplifying further:

vmax / vmin = √(1 / 2)

Taking the square root of 1/2:

vmax / vmin = 1 / √2

Rationalizing the denominator:

vmax / vmin = √2 / 2

Finally, we can see that vmax is twice vmin:

vmax = 2 × vmin

Therefore, to transition from a circular orbit of radius R to an elliptical orbit with rmin = R and rmax = 2R, the velocity v must be increased by a factor of 2.

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Answer:

B. blocks 2 & 3.

Explanation:

Block 1 has equal & opposite forces acting on it.

Block 2 has 5N on one side, 3N on the other. It will move in the direction the 5N of force is pushing.

Block 3 has no opposing force.

chemical reaction for fossil fuels:combustion of fuels.

Difference between biomass and fossil fuels:how much carbon dioxide is produced

Comparing biomass with other renewable energy sources:does not have as much energy potential as fossil fuels.

Making energy choices locally: biomass

it should be rising and converging

The global winds and moisture belts indicate that large amounts of rainfall occur at the Earth's equator because air is rising and converging.

The equator is a large circle that circles the planet Earth, lying in a plane perpendicular to the axis of the planet and being equally spaced from all four geographic poles.

Rainfall in equatorial regions averages 4000mm per year. Every other raining produces about 22 days of precipitation in a month. The equatorial regions have higher temperatures because solar radiation produces a lot of heat there.

The cold air filters down into the lower levels of the atmosphere because the hot air is less dense here than the cold air. The tropical regions become warmer as a result. In the tropical rain belt, the tropical climate predominates.

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Based on the given information of a lattice parameter and powder X-ray wavelength, the crystal structure can be determined by considering only the FCC and BCC structures as possibilities.

The lattice parameter, denoted as 'a,' represents the distance between the lattice points in a crystal structure. In this case, the given value of 'a' is 0.4997 nm. To determine the crystal structure, we need to compare this lattice parameter with the characteristic values of the FCC (face-centered cubic) and BCC (body-centered cubic) structures.

For the FCC structure, the relationship between the lattice parameter 'a' and the radius of the atoms or ions in the structure is given by a = 4√2r, where 'r' represents the atomic or ionic radius. Similarly, for the BCC structure, the relationship is a = 4√3r.

By rearranging the equations, we can solve for the radius 'r.' For the FCC structure, r = a/(4√2), and for the BCC structure, r = a/(4√3). Substituting the given lattice parameter 'a' into these equations, we can calculate the corresponding radii for each structure.

Next, we compare the calculated radii with the typical atomic or ionic radii for different elements. If the calculated radius matches closely with the known radius of an element, then that element is likely to form the crystal structure.

Lastly, to confirm the crystal structure, we can consider the powder X-ray wavelength (λ) provided. The X-ray diffraction pattern obtained from the powder X-ray experiment can help identify the characteristic peaks for different crystal structures. By comparing the observed diffraction pattern with the known patterns for FCC and BCC structures, we can determine the crystal structure based on the closest match.

In conclusion, by calculating the radii for FCC and BCC structures using the given lattice parameter, and by analyzing the X-ray diffraction pattern obtained from the powder X-ray experiment, the crystal structure can be determined as either FCC or BCC.

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Answer:

A malleable material is one in which a thin sheet can be easily formed by hammering or rolling. ... In contrast, ductility is the ability of a solid material to deform under tensile stress.

Answer:

The correct option is (C).

Explanation:

The distance between two charges, [tex]d=10^{-8}\ m[/tex]

We need to find the magnitude of the electrostatic force between two electrons. The formula for the electric force between charges is given by :

[tex]F=\dfrac{kq^2}{r^2}\\\\=\dfrac{9\times 10^9\times (1.6\times 10^{-19})^2}{(10^{-8})^2}\\\\=2.304\times 10^{-12}\ N[/tex]

So, the magnitude of force is equal to [tex]2.30\times 10^{-12}\ N[/tex].

Answer:

V = f x λ

Explanation:

The options are confusing

Some diversification benefits can be achieved by combining securities in a portfolio as long as the correlation between the securities isThe correct answer is C. Between 0 and 1.

Diversification benefits can be achieved by combining securities in a portfolio as long as the correlation between the securities is between 0 and 1. Correlation measures the degree to which two securities move in relation to each other. A correlation of 1 indicates a perfect positive correlation, where the securities move in perfect tandem. A correlation of less than 1 indicates a less than perfect positive correlation, where the securities move somewhat together but not completely. When the correlation is between 0 and 1, it means that the securities have some degree of independence and tend to move differently from each other. This allows for diversification benefits as losses in one security may be offset by gains in another, reducing overall portfolio risk.

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The figure skater spinning with her arms held straight out will have greater rotational speed at her fingertips compared to her shoulders.

When the skater extends her arms straight out, the moment of inertia increases as the mass is distributed farther from the axis of rotation (her body).

According to the conservation of angular momentum, the product of moment of inertia and angular velocity remains constant unless an external torque acts on the system.

Since the moment of inertia increases when her arms are extended, the angular velocity must decrease to maintain the constant angular momentum.

As a result, the rotational speed is higher at her fingertips because they have a larger distance from the axis of rotation compared to her shoulders.

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Bethany weighs 460 N and she is lying in a hammock which is suspended by ropes that are tied to two trees. The left rope makes an angle of 45° with the ground and the right one makes an angle of 30°.  Therefore, the tension in the left rope is approximately 325 N (rounded to 3 significant figures) and the tension in the right rope is approximately 362 N (rounded to 3 significant figures).

We need to find the tension in the left and right ropes. We will use the trigonometric functions to solve the problem. Let us assume that T1 is the tension in the left rope and T2 is the tension in the right rope. Now, let us resolve the forces acting on the hammock horizontally and vertically using trigonometry. From the diagram above, we can see that the weight of Bethany (460 N) acts downwards, so we can resolve this force vertically.

We get the following equations:∑ Fx = T1 cos 45° - T2 cos 30° = 0 (∵ hammock is not moving horizontally)

∑ Fy = T1 sin 45° + T2 sin 30° - 460 N = 0 (∵ hammock is not moving vertically)

Now we can solve the two equations simultaneously to get T1 and T2.

T1 cos 45° - T2 cos 30° = 0  ...

(1)T1 sin 45° + T2 sin 30° - 460 N = 0  ...

(2)Multiplying equation (1) by sin 45° and equation (2) by cos 30°, we get:

T1 sin 45° cos 30° - T2 cos 30° cos 45° = 0 ...

(1')T1 sin 45° cos 30° + T2 sin 30° cos 30° = 460 N cos 30°  ...

(2')Adding equations (1') and (2'), we get:

T1 sin 45° cos 30° = 460 N cos 30°T1 = 460 N cos 30° / sin 45°T1 = 460 N / √2

T2 = T1 cos 45° / cos 30°T2 = (460 N / √2) (cos 45° / cos 30°)T2 = 362 N.

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Answer:

Yes

Explanation:

sorry if im wrong

The expression that represents the number of seconds required for a single swing is 2.5 seconds.

Hence, the correct option is C.

The number of seconds required for a single swing of a pendulum is half of the time it takes to complete a full swing.

Given that the pendulum makes full swings in 5 seconds, the expression for the number of seconds required for a single swing would be

5 seconds / 2 = 2.5 seconds

Therefore, the expression that represents the number of seconds required for a single swing is 2.5 seconds.

Hence, the correct option is C.

The given is incomplete and the complete question is '' A pendulum swings back and forth with a repeating motion. the pendulum makes full swings in 5 seconds. which expression below is the number of seconds required for a single swing

A. 3 seconds

B. 2.5 seconds

C. 5 seconds

D. 4 seconds ''.

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Answer:

For which the reasoning of the boy is correct for small heights, but as height increases his analysis is not correct.

Explanation:

The force of gravity comes from Newton's second law with the force the universal attraction

         F = ma

         F = [tex]G \frac{m_1 M}{(R_e +h)^2}[/tex]

we substitute

          [tex]G \frac{m_1 M}{ (R_e+ h)^2}[/tex] = m₁ a

where Re is the radius of the Earth 6.37 106 m

          a = [tex]G\frac{M}{R_e^2} \ ( 1 + \frac{h}{R_e})^{-2}[/tex]

In general, the height is much less than the radius of the earth, therefore the term ha / Re is very small and we can use a series expansion leaving only the first fears.

             (1 + x)⁻² = 1 -2x + [tex]\frac{2 \ 1}{2!}[/tex]  x²

we substitute

          a = g₀ ([tex]1 - 2 \frac{h}{R_e}[/tex] )

with

         g₀ = [tex]G \frac{M}{R_e^2}[/tex]

let's launch the expression.

* For small height compared to the radius of the earth we can neglect the last term

          g = g₀

* For height comparable to the radius of the Earth

          g = g₀  [tex](1 - \frac{2h}{Re} )[/tex]

We see that the acceleration of gravity is decreasing.

For which the reasoning of the boy is correct for small heights, but as height increases his analysis is not correct.

The student's reasoning gone wrong when the analysis is undertaken for the increasing heights, to drop the object.

The given problem is based on the concept of gravity and gravitational force. The force of gravity comes from Newton's second law with the force the universal attraction as,

F = ma

[tex]F=G\dfrac{mM}{(R+h)^{2}}\\\\\\ma = G\dfrac{mM}{(R+h)^{2}}[/tex]

Here, a is the linear acceleration, m is the mass of object, M is the mass of Earth, R is the radius of Earth and h is the height from where the objects will be dropped. Then,

[tex]a = \dfrac{GM}{R^{2}} \times(1+h/R)^{-2}[/tex]

In general, the height is much less than the radius of the earth, therefore the term h/ R is very small, hence can be neglected.

[tex]a = \dfrac{GM}{R^{2}}\\\\a=g = \dfrac{GM}{R^{2}}[/tex]

g is the gravitational acceleration.

For small height compared to the radius of the earth we can neglect the last term as,

a = g

And for the height comparable to radius of Earth,

[tex]a = \dfrac{GM}{R^{2}} \times(1+h/R)^{-2}\\\\a=g \times(1+h/R)^{-2}[/tex]

Clearly, the acceleration of gravity is decreasing, for which the reasoning of the boy is correct for small heights, but as height increases his analysis is not correct.

Thus, we can conclude that the student's reasoning gone wrong when the analysis is undertaken for the increasing heights, to drop the object.

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A 10 kg mass slides down a flat hill that makes an angle of 10 degrees with the horizontal. Therefore, the resultant force on the sled is option (c) 97N.

If friction is negligible, the resultant force on the sled will be calculated below:

We know that gravitational force can be broken into two components - force parallel to the slope and force perpendicular to the slope.

The parallel component is given by

Fg * sin θ = 10*9.8*sin10 = 16.87 N.

The perpendicular component is given by

Fg * cos θ = 10*9.8*cos10 = 96.94 N.

The total force acting on the sled is the vector sum of the two components: Resultant force = √(16.87² + 96.94²) = 97 N.

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The total work performed around the thermodynamic cycle in Figure 7 is 350 Joules.
In a thermodynamic cycle, the total work performed is equal to the net area enclosed by the cycle on a pressure-volume (PV) diagram. From the given figure, we can observe that the cycle consists of two quasi-static processes: Process 1-2 and Process 2-3.

In Process 1-2, the system undergoes an expansion at constant pressure, represented by the horizontal line between points 1 and 2 on the PV diagram. As the volume increases, work is done by the system, and the work done in this process is given by the equation W_1-2 = PΔV = 2 * 50 = 100 Joules (where P is the constant pressure and ΔV is the change in volume).

In Process 2-3, the system undergoes compression at constant volume, represented by the vertical line between points 2 and 3 on the PV diagram. Work is done on the system during this process, and the work done in this process is given by the equation W_2-3 = -PΔV = -3 * 50 = -150 Joules (where P is the constant pressure and ΔV is the change in volume).

The total work performed around the cycle is the sum of the work done in each process, i.e., 100 Joules + (-150 Joules) = -50 Joules.
The total work performed around the thermodynamic cycle in Figure 7 is -50 Joules.

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Answer:

The bright blue and black colors represent the following:

Constructive and destructive interference are represented by the blue and black colors, respectively. When two water waves collide constructively, the resultant wave is bright blue, while when they collide destructively, the resultant wave is black in color.

Explanation:

   When two propagating waves with the same frequency (say, [tex]\nu[/tex]) and wavelength (say,[tex]\lambda[/tex]) but slightly different amplitudes (say, A 1 and A 2) traveling in the same direction interfere or are superimposed on each other (that is incident at the same point or object), a third resultant wave with a different amplitude (increased or decreased) but same wavelength and frequency is generated.  

The direction difference between the two waves determines whether they intervene constructively (increasing the amplitude of the resultant wave) or destructively (increasing the amplitude of the resultant wave) (decreased amplitude of the resultant wave). To put it another way, when the difference in direction between the two waves is of the form -

      [tex]\Delta x = n\lambda , n=0,1,2,.....[/tex] is the order of interference.

The two waves are then assumed to be in phase, and the interference is constructive, resulting in the resultant wave having a larger amplitude (which is the sum of the two amplitudes [tex]A_1 +A_2[/tex]  also known as a maxima). When the difference in direction between the two waves is in the form -

  [tex]\Delta x = (2n-1)\frac{\lambda}{2} , n=0,1,2,.....[/tex] is the order of interference.

The two intervening waves are then said to be out of phase, and the interference is disruptive, resulting in the resultant wave having a lower amplitude (which is the difference between the two amplitudes [tex]A_1+A_2[/tex], also known as a minima).

Hence , the graphical representation of constructive (blue )and destructive (black) is attached.

Answer:

a. 0.947 m/s^2

b. 1304.54 N

c. 0.0966

Explanation:

mass of car = 13500 N = 13500/9.8 = 1377.55 kg

velocity = 50 km/h = 50,000 m/h = 13.9 m/s

raidus = 204 m

a. centripetal acceleartion = v^2/r = 13.9^2/204 = 0.947 m/s^2

b. centripetal force = m*centripetal acceleration = 1377.55 * 0.947 = 1304.54 N

c. In order for the car to round the curve safely, static friction = centripetal force

static friction = coefficient of friction (mu) * mg = mu* 1377.55*9.8 = 13500mu

13500mu = 1304.54

mu = 1304.54/13500 = 0.0966

The acceleration, force and coefficient of friction is required.

Centripetal acceleration is [tex]0.965\ \text{m/s}^2[/tex]

Centripetal force is [tex]1328\ \text{N}[/tex]

Coefficient of friction is [tex]0.1[/tex]

N = Weight of car = 13500 N

v = Velocity = [tex]50=\dfrac{50}{3.6}=13.89\ \text{m/s}[/tex]

r = Radius = [tex]2\times 10^2\ \text{m}[/tex]

m = Mass of car = [tex]\dfrac{N}{g}[/tex]

g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]

Centripetal acceleration is

[tex]a_c=\dfrac{v^2}{r}\\\Rightarrow a_c=\dfrac{13.89^2}{2\times 10^2}\\\Rightarrow a_c=0.965\ \text{m/s}^2[/tex]

Force is given by

[tex]F_c=ma_c\\\Rightarrow F_c=\dfrac{N}{g}a_c\\\Rightarrow F_c=\dfrac{13500}{9.81}\times 0.965\\\Rightarrow F_c=1328\ \text{N}[/tex]

Coefficient of friction is given by

[tex]\mu=\dfrac{F_c}{N}\\\Rightarrow \mu=\dfrac{1328}{13500}\\\Rightarrow \mu=0.098\approx 0.1[/tex]

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Answer:

C hope it helps

call the client and inform her that she was incorrectly charged.

Answer:

The answer is C. call the client and inform her that she was incorrectky charged

Explanation:

The mass of a neutral atom of ₈O¹⁸ is approximately equal to the sum of the masses of 8 atoms of ₁H¹ and 10 neutrons.

Given that the nucleus of ₈O¹⁸ is formed by 8 protons and 10 neutrons.

₈O¹⁸ = 8 protons(p) + 10 neutrons(n)

The mass of an atom is defined as the sum of the nucleons of the atom.

Nucleons are the general word for protons and neutrons since they are both found in the nucleus. Nucleons are hence the scientific term for the subatomic particles found in the atom's nucleus.

So,

Mass of the neutral atom of ₈O¹⁸ = (8 x mp) + (10 x mn)

m(₈O¹⁸) = (8 x 1.007276u) + (10 x 1.008665u)

m(₈O¹⁸) = 8.058208 + 10.08665

m(₈O¹⁸) = 18.144858 u

Also,

Mass of 8 atoms of ₁H¹ = 8 x m(₁H¹)

Mass of 8 atoms of ₁H¹ = 8 x 1.007825u

Mass of 8 atoms of ₁H¹ = 8.0626 u

So,

Mass of 8 atoms of ₁H¹ + 10 mn = 8.0626 + 1.008665

M = 18.9291 u

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n = 3, ℓ = 1, mℓ = 1, ms = -1 is an impossible set of quantum numbers.

What are quantum numbers?

Quantum numbers are a set of values used to describe the unique energy states and properties of electrons in an atom. They provide a way to distinguish and characterize the different electron orbitals within an atom.

Among the given options:

a. n = 3, ℓ = 2, mℓ = 1, ms = -½

b. n = 3, ℓ = 1, mℓ = 1, ms = -1

c. n = 2, ℓ = 0, mℓ = 0, ms = -½

d. n = 1, ℓ = 0, mℓ = 0, ms = -½

Option (a) represents a valid set of quantum numbers. However, options (b), (c), and (d) are impossible sets of quantum numbers.

For option (b), the value of mℓ is not within the allowed range for the given ℓ value. In this case, ℓ = 1, which means that mℓ can have values -1, 0, or 1. The value of mℓ = 1 is outside this range.

For options (c) and (d), the values of n and ℓ are not consistent. According to the rules of quantum numbers, the principal quantum number (n) should be greater than or equal to the azimuthal quantum number (ℓ). However, in both options (c) and (d), the value of n is lower than ℓ, which is not possible.

Therefore, the correct answer is option (b), as it represents an impossible set of quantum numbers.

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An automobile engine slows down from 4,087 rpm to 1,830 rpm in 1,419 revolutions the magnitude of the angular acceleration of the automobile engine is approximately 77.75 rad/s².

To calculate the magnitude of the angular acceleration, we can use the formula:

Angular acceleration (α) = (ω2 - ω1) / (t2 - t1)

where:

ω1 and ω2 are the initial and final angular velocities, respectively, and

t1 and t2 are the initial and final times, respectively.

Initial angular velocity ω1 = 4087 rpm

Final angular velocity ω2 = 1830 rpm

Number of revolutions (n) = 1419

First, we need to convert the angular velocities from rpm to radians per second (rad/s):

ω1 = (4087 rpm) * (2π rad/1 min) * (1 min/60 s) ≈ 426.97 rad/s

ω2 = (1830 rpm) * (2π rad/1 min) * (1 min/60 s) ≈ 191.46 rad/s

Next, we can calculate the time interval (t2 - t1) using the number of revolutions and the initial and final angular velocities:

t2 - t1 = (n / ω2) - (n / ω1)

t2 - t1 = (1419 / 191.46) - (1419 / 426.97) ≈ 3.3 s

Finally, we can calculate the magnitude of the angular acceleration:

α = (ω2 - ω1) / (t2 - t1)

α = (191.46 rad/s - 426.97 rad/s) / (3.3 s)

α ≈ -77.75 rad/s²

Therefore, the magnitude of the angular acceleration of the automobile engine is approximately 77.75 rad/s².

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When a rocket is launched straight up from the Earth's surface, its speed gradually decreases as it moves away from the planet.

However, it never truly reaches a constant speed when it is very far away from the Earth. Instead, its speed continues to decrease due to the gravitational pull of other celestial bodies in space, such as the Sun and other planets. Therefore, it is not possible to determine the rocket's exact speed when it is very far away from the Earth without additional information about the rocket's trajectory, the effects of other gravitational forces, and the time elapsed since the launch. The exact speed when the rocket is very far away would depend on various factors, including the rocket's design, propulsion system, and the duration of its engine burn.

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Planet A exerts a force on planet B, the magnitude and direction of the gravitational force planet B exerts on planet A the gravitational force exerted by planet B on planet A is the same as the magnitude of the gravitational force exerted by planet A on planet B

Newton's third law states that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. Hence, if planet A exerts a gravitational force on planet B, then planet B exerts an equal and opposite gravitational force on planet A.The magnitude of the gravitational force exerted by planet B on planet A is the same as the magnitude of the gravitational force exerted by planet A on planet B, this is according to the law of universal gravitation,

This law states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The direction of the gravitational force exerted by planet B on planet A is towards planet B's center, just as the direction of the gravitational force exerted by planet A on planet B is towards planet A's center. Therefore, we can say that the magnitude and direction of the gravitational force planet B exerts on planet A is equal and opposite to the gravitational force planet A exerts on planet B

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The speed οf the ball when it reaches the lοwest pοint οf the track, rοlling withοut slipping is √10/7g(R-r).

Speed is a scalar quantity that measures hοw fast an οbject is mοving, withοut cοnsidering its directiοn. Speed is typically expressed in units such as meters per secοnd (m/s), kilοmeters per hοur (km/h), οr miles per hοur (mph).

Given:

The radius οf the ball is r.

The radius οf the track is R.

The acceleratiοn due tο gravity is 9.18 m/s².

The mοment οf inertia οf the spherical ball can be expressed as:

I=2/5m/r²

It is given that the ball is rοlling withοut slipping. The speed οf the ball can be expressed as:

v=rω

At the lοwest pοsitiοn οf the track, the ball has bοth types οf speed, namely angular and linear speed.

The tοtal energy οf the ball in the vertical circle can be expressed as:

cEₜ= Eᵦ+ K.Eₜ+ K.Eᵣ

mgR= mgr+ (1/2)mv²+ (1/2)Iω²

mg(R-r)=  (1/2)mv²+ (1/2)* (2/5) mr²ω²

g(R-r)= (1/2)v²+ (1/5)v²

Here,

Eₜ is the tοtal energy οf the ball οn the track,

Eᵦ is the ball's energy in the vertical circle at the highest pοint,

K.Eₜ is the translatiοnal kinetic energy οf the ball,

K.Eᵣ is the rοtatiοnal kinetic energy οf the ball, and g is the acceleratiοn due tο gravity.

The abοve equatiοn can be further sοlved as:

cg(R-r)= (7/10)v²

v²= (10/7)g (R-r)

v= √(10/7)g (R-r)

Therefοre, the speed οf the ball when it reaches the lοwest pοint οf the track is √10/7g(R-r).

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