The 75. 0 kg hero of a movie is pulled upward with a constant acceleration of 2. 00 m/s2 by a rope. What is the tension on the rope?


585N



75. 0N



885N



11. 8N

Explanation:

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If an inductor must be selected for a circuit that will exactly match the reactance of a 711.3 nf capacitor in a 120 v, 58.0 hz source, the required inductance for the circuit is 65.0 millihenries.

To determine the required inductance for a circuit that matches the reactance of a 711.3 nf capacitor in a 120 V, 58.0 Hz source, we need to use the formula for calculating reactance.

Reactance is the opposition that an inductor or capacitor offers to alternating current, and it is measured in ohms. The reactance of an inductor is given by the formula X₁ = 2πfL, where X₁ is the inductive reactance in ohms, f is the frequency in Hertz, and L is the inductance in Henrys.

The reactance of a capacitor is given by the formula X₂ = 1/(2πfC), where X₂ is the capacitive reactance in ohms, f is the frequency in Hertz, and C is the capacitance in farads.

To match the reactance of the capacitor, we need to calculate the inductance required to cancel out the capacitive reactance. Therefore, we need to set X₁ equal to X₂ and solve for L.

X₁ = X₂

2πfL = 1/(2πfC)

L = 1/(4π^2f^2C)

Substituting the given values, we get:

L = 1/(4π^2(58.0 Hz)^2(711.3 nF))

L = 65.0 mH

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The efficiency of the bike can be calculated by dividing the work output by the energy input and multiplying the result by 100%. In this case, the bike is 91.67% efficient.

The efficiency of a machine is defined as the ratio of the work output to the energy input. In this case, the energy input is given as 600 joules per minute, and the work output is 550 joules.

Therefore, the efficiency of the bike can be calculated using the following formula:

Efficiency = (Work output / Energy input) x 100%

Substituting the given values, we get:

Efficiency = (550 / 600) x 100%

Efficiency = 0.9167 x 100%

Efficiency = 91.67%

This means that the bike is 91.67% efficient, which is the percentage of the energy input that is converted into useful work output. The remaining energy is lost as heat due to friction, air resistance, and other factors.

Therefore, the efficiency of the bike can be improved by reducing these losses through proper maintenance and adjustments.

In summary, the efficiency of the bike can be calculated by dividing the work output by the energy input and multiplying the result by 100%. In this case, the bike is 91.67% efficient.

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The motion of a 0.500-kg glider attached to an ideal spring with a force constant of k=450m can be analyzed in terms of mechanical energy. Mechanical energy is the sum of kinetic energy and potential energy, and is conserved in a closed system with no external forces acting on it.

As the glider moves back and forth on the spring, its kinetic energy varies with its speed and its potential energy varies with its position. At any point in its motion, the total mechanical energy of the glider is equal to the sum of its kinetic and potential energy.

At the maximum compression of the spring, the glider has zero velocity and maximum potential energy. As it moves away from this point, the spring begins to expand and the glider begins to move faster, converting potential energy into kinetic energy. At the point where the spring is fully extended, the glider has maximum velocity and zero potential energy.

As the glider continues to move back towards the spring's rest position, it begins to slow down and convert kinetic energy back into potential energy. At the point of maximum compression again, the glider has zero velocity and maximum potential energy once more.

Throughout its motion, the total mechanical energy of the glider remains constant, as there are no external forces acting on the system. This means that the sum of the kinetic and potential energy at any point in its motion is equal to the total mechanical energy of the system.

In summary, the mechanical energy of a glider attached to an ideal spring can be analyzed at any point in its motion by considering the conversion of potential energy into kinetic energy and vice versa. The total mechanical energy of the system is constant throughout its motion, making it a useful tool for analyzing the behavior of the glider on the spring.

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The angular momentum of a 265 kg motorcycle traveling at 25 m/s around a circular curve with a radius of 500 m is [tex]3,312,500 \;kg.m^2/s.[/tex]

To calculate the angular momentum of the motorcycle, we need to first find its angular velocity. Since the motorcycle is traveling around a circular curve, we can use the formula:

[tex]v = r\omega[/tex]

where v is the velocity of the motorcycle, r is the radius of the curve, and ω is the angular velocity.

Rearranging this formula to solve for ω, we get:

[tex]\omega = v/r[/tex]

Substituting the values given, we get:

[tex]\omega = 25 \;m/s \;/ \;500 m = 0.05 \;rad/s[/tex]

Next, we can use the formula for angular momentum:

[tex]L = I\omega[/tex]

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

For a point mass moving in a circular path, the moment of inertia is simply mr², where m is the mass of the motorcycle and r is the radius of the curve.

Substituting the values given, we get:

[tex]L = (265 \;kg)(500 \;m)^2(0.05 \;rad/s)[/tex]

[tex]L = 3,312,500 \;kg.m^2/s[/tex]

Therefore, the angular momentum of the motorcycle is [tex]3,312,500 \;kg.m^2/s.[/tex]

In summary, the angular momentum of a 265 kg motorcycle traveling at 25 m/s around a circular curve with a radius of 500 m is [tex]3,312,500 \;kg.m^2/s.[/tex]

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The period of a simple pendulum of length 1m on a massive planet is 1 sec. The acceleration due to gravity on that planet is 39.48 m/s^2.

A simple pendulum's period is given by:

T = 2π √(L/g)

Where T is the pendulum's period, L is its length, and g is the acceleration due to gravity.

In this scenario, the pendulum's period is one second and its length is one metre.

So, from above equation, we have:

1 = 2π √(1/g)

Squaring both sides, we get:

1^2 = (2π)^2 (1/g)

Simplifying, we get:

g = (4π^2)/1 = 39.48 m/s^2

Therefore, the acceleration due to gravity on the massive planet is 39.48 m/s^2.

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Answer:

The archerfish is a type of fish well known for its ability to catch resting insects by spitting a jet of water at them.

Explanation:

The new speed of the system when the ball is caught is approximately 0.025 m/s

To solve this problem, we will use the conservation of momentum equation:

MaVa + MbVb = (Ma + Mb)(Va+b)

where Ma is the mass of the football (0.257 kg), Va is the velocity of the football (9.76 m/s), Mb is the mass of the receiver and hovercraft (98.6 kg), and Vb is the initial velocity of the receiver and hovercraft (0 m/s, since it is stationary).

0.257 kg * 9.76 m/s + 98.6 kg * 0 m/s = (0.257 kg + 98.6 kg) * (Va+b)

2.50632 kg*m/s = 98.857 kg * (Va+b)

Now, we will solve for Va+b:

Va+b = 2.50632 kg*m/s / 98.857 kg

Va+b ≈ 0.025 m/s

So, the new speed of the system when the ball is caught is approximately 0.025 m/s, rounded to three decimal places.

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The resistance of the heating element is 9 Ohms

Ohm's law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) between them. Mathematically, this can be expressed as:

V = IR

In this scenario, we are given the power (P) and current (I) of a heater, and we are asked to find its resistance (R). Power can be calculated using:

P = IV

where V is the voltage across the heater. Since we are not given the voltage, we can rearrange Ohm's law to solve for the resistance:

R = V/I

Substituting the formula for power into this equation, we get:

R = (V/I) = (P/I²)

Substituting the given values of power and current, we get:

R = (325 W) / (6.0 A)² = 9.0 Ohms

The correct answer is (D).

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Answer:

7086.9 feet.

Explanation:

We can see that the two triangles formed by the plane and the cars are similar, because they share a common angle (90 degrees) and have corresponding angles that are equal (the angles of depression). Therefore, we can use the proportionality of corresponding sides to find the distance between the cars. Let x be the distance from the plane to the car with 35 degrees angle of depression, and y be the distance from the plane to the car with 52 degrees angle of depression. Then we have:

The answer is 7086.9 feet.

What lightning has in common with the shock you receive when you touch a doorknob is that both phenomena involve the transfer of electric charges between two objects or areas with different electrical potentials. This process is known as electrostatic discharge (ESD).

1. Formation of electric charge: In both cases, there is a buildup of electric charges due to friction or other processes. With lightning, this occurs within clouds, where ice particles collide and generate static electricity. In the case of the doorknob shock, static electricity builds up on your body as you walk across a carpet, for example.

2. Difference in electric potential: Once there is a significant charge buildup, there is a difference in electric potential between the charged object and another object or area with an opposite charge.

For lightning, this difference occurs between the cloud and the ground, while for the doorknob shock, it occurs between your body and the metal doorknob.

3. Discharge: When the electric potential difference is large enough, a sudden and rapid discharge of the built-up charges takes place. This results in the visible lightning bolt or the spark and shock experienced when touching the doorknob.

4. Release of energy: In both cases, the discharge of electric charges releases energy in the form of light, heat, and sound. This energy release is what causes the bright flash of lightning and the audible snap of a doorknob shock.

In summary, lightning and the shock you receive when touching a doorknob are similar because they both involve the buildup and discharge of electric charges between objects or areas with different electrical potentials, ultimately releasing energy in the process.

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Answer:

The lightning struck 1,360 meters away

Explanation:

1. List knowns

Speed of sound = 340 m/s

Time = 4 s

2. Find formula that uses above knowns

Speed = Distance / Time

Distance = Time x Speed

3. Substitute

Distance = 4 s x 340 m/s

Distance = 1360 meters

To make the concert F sound right to the audience, Sammy Hagar and the band should play the note at a frequency of 607 Hz.

The frequency that the audience will hear, denoted as f', is related to the frequency of the source, f, by the formula: f' = f (v + u) / (v - u)

where v is the speed of sound, u is the speed of the observer relative to the medium, and in this case, v = 343 m/s and u = -32 m/s.

When the stage is moving toward the audience, the relative speed of the sound waves is increased, so the frequency heard by the audience is higher. Using the above formula: f' = 540 Hz (343 + 32) / (343 - 32) = 607 Hz

Therefore, to make the concert F sound right to the audience, Sammy Hagar and the band should play the note at a frequency of 607 Hz.

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One material resource that is potentially renewable if managed well is wood.

Wood can be obtained from trees, which are a renewable resource if they are harvested and replanted in a sustainable manner.

Sustainable forest management practices ensure that forests are used in a way that meets the needs of the present without compromising the ability of future generations to meet their own needs.

Wood is used for various purposes, such as construction, furniture, paper, and energy production. By managing forests well, we can ensure a continuous supply of wood for these purposes.

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The net torque on the Ferris wheel is approximately 1,500,000 N*m.

To find the net torque on the Ferris wheel, we'll need to use the following formula: τ = I * α, where τ represents torque, I is the moment of inertia, and α is the angular acceleration.

First, we need to find the angular acceleration (α). Since the Ferris wheel accelerates from rest (initial angular speed = 0) to an angular speed of 20 rad/s in 12 s, we can use the formula: α = (final angular speed - initial angular speed) / time.

α = (20 rad/s - 0 rad/s) / 12 s = 20/12 rad/s² = 5/3 rad/s²

Next, we'll find the moment of inertia (I) for a circular disk with a mass (m) of 2000 kg and a radius (r) of 30 m: I = (1/2) * m * r².

I = (1/2) * 2000 kg * (30 m)² = 1000 kg * 900 m² = 900,000 kg*m²

Now, we can find the net torque (τ) using the formula: τ = I * α.

τ = 900,000 kg*m² * 5/3 rad/s² ≈ 1,500,000 N*m

So, the net torque on the Ferris wheel is approximately 1,500,000 N*m.

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The approximate electrostatic force between two protons each having a charge of +1. 6 x 10-19 C separated by a distance of 1. 0 × 10–6 meter A) 2.3 × 10^–16 N and repulsive.

To calculate the electrostatic force between two protons, we can use Coulomb's Law:

F = (k * q1 * q2) / r^2

where F is the electrostatic force, k is Coulomb's constant (8.99 × 10^9 N m^2 C^−2), q1 and q2 are the charges of the two protons, and r is the distance between them.

Given: q1 = q2 = +1.6 × 10^-19 C, r = 1.0 × 10^-6 m

Now, plug the values into the formula:

F = (8.99 × 10^9 N m^2 C^−2 * (1.6 × 10^-19 C)^2) / (1.0 × 10^-6 m)^2

F ≈ 2.3 × 10^-16 N

Since both charges are positive, the electrostatic force will be repulsive. Therefore, the correct answer is:

A) 2.3 × 10^–16 N and repulsive

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In order to determine how many coulombs are in a typical car battery's 70 amp-hours of charge, we first need to understand the relationship between amps and coulombs.

Amps measure the flow of electric current, while coulombs measure the amount of electric charge. One coulomb is equal to the amount of charge transported by a current of one ampere in one second.

Therefore, to convert amp-hours to coulombs, we need to multiply the number of amp-hours by the number of seconds in an hour (3,600) and by the number of coulombs per ampere-second (1). This gives us:

70 amp-hours x 3,600 seconds/hour x 1 coulomb/ampere-second = 252,000 coulombs

So a typical car battery provides 252,000 coulombs of charge. This is important information because it helps us understand the amount of electrical energy available for use in the various components of the vehicle, such as the headlights, windshield wipers, and sound system.

The alternator plays a critical role in maintaining and replenishing the charge on the car's battery, which in turn ensures that these components can continue to operate effectively.

Overall, the interplay between mechanical and electrical systems in a motor vehicle is a fascinating and complex topic that requires a deep understanding of physics, engineering, and technology.

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Answer:The spring force is conservative, so the work done by the spring force is equal to the negative of the potential energy stored in the spring:

U = -1/2 k x^2

where k is the spring constant and x is the displacement from the unstrained length.

The initial compression of the spring is 4.10 mm = 0.00410 m, and the additional compression is 6.10 mm = 0.00610 m. The total compression of the spring is therefore x = 0.00410 m + 0.00610 m = 0.0102 m.

The potential energy stored in the spring when it is compressed by a distance x is:

U = -1/2 k x^2

Substituting the given values, we get:

U = -1/2 (216 N/m) (0.0102 m)^2

U = -0.0112 J

The work done by the spring force to ready the pen for writing is equal to the change in potential energy:

W = U_final - U_initial

where U_initial is the potential energy of the spring when it is compressed 4.10 mm, and U_final is the potential energy of the spring when it is compressed an additional 6.10 mm.

U_initial = -1/2 (216 N/m) (0.00410 m)^2 = -0.000090 J

U_final = -1/2 (216 N/m) (0.0102 m)^2 = -0.0112 J

W = U_final - U_initial

W = (-0.0112 J) - (-0.000090 J)

W = -0.0111 J

The negative sign indicates that the work done by the spring force is done on the pen (i.e. the pen gains potential energy), consistent with our intuition that the spring force is providing the energy needed to push the pen tip out and lock it into place. Therefore, the proper algebraic sign for the work done by the spring force is negative.

Explanation:

The gravitational force between the two masses is approximately 1.96 x 10⁻⁹ N. Option B is correct.

The gravitational force between two masses can be calculated using the formula;

F=G x (m₁ x m₂) / r²

Where F is the gravitational force, G is the gravitational constant, m₁ and m₂ are the masses of the two objects, and r is the distance between their centers of mass.

In this case, m₁ = 4.0 kg, m₂ = 7.0 kg, r = 1.0 m, and G = 6.67 x 10⁻¹¹ N x m²/kg². Plugging these values into the formula gives;

F = (6.67 x 10⁻¹¹ N x m²/kg²) x (4.0 kg x 7.0 kg) / (1.0 m)²

F = 1.96 x 10⁻⁹ N

Therefore, the gravitational force is 1.96 x 10⁻⁹ N.

Hence, B. is the correct option.

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--The given question is incomplete, the complete question si

"A 4.0 kg mass is 1.0 m away from a 7.0 kg mass. What is the gravitational force between the two masses? (Remember to use the gravitational constant, G = 6.67 x 10-11 N x m2/ kg2, in your calculation.) A) 6.67 x 10 -11 N B) 1.9 x 10 -9N C) 6.67 x 10 10N D) 3.8 N."--

The type of radioactive decay of carbon to nitrogen is beta-minus decay.

A kind of radioactive decay called beta-minus involves the emission of electrons and antineutrinos from the nucleus as well as the transformation of neutrons into protons, which raises the atomic number of the atom..

This increases the atomic number of the nucleus by one and leaves the mass number unchanged. The question mentions the decay of carbon-14 (C) to nitrogen-14 (N) as an example of beta-minus decay in the given reaction.

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Complete question - What type of radioactive decay is this process? An example of?

¹⁴C → ¹⁴N + e⁻ + v

The wavelength of the sound wave is approximately 1.5 meters.

1 pt: Knowns/Unknown:
- Frequency (f) = 230 beats per second (Hz)
- Speed of sound (v) = 340 m/s
- Wavelength (λ) = Unknown

1 pt: Write the equation:
The equation relating the speed of sound, frequency, and wavelength is: v = f * λ

1 pt: Solve:
To find the wavelength (λ), rearrange the equation: λ = v / f

1 pt: Correct answer (rounded to one decimal place):
λ = 340 m/s / 230 Hz ≈ 1.5 m

The wavelength of the sound wave is approximately 1.5 meters.

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The repeated association of the drug injection with the small examination room has led to classical conditioning, resulting in an increased heart rate response to just being in the room.

This phenomenon can be explained through classical conditioning. Classical conditioning is a type of learning in which an organism learns to associate two stimuli together, resulting in a change in behavior.

In this case, the drug injection is the unconditioned stimulus (UCS) that naturally elicits an unconditioned response (UCR) of an increased heart rate.

However, over time, the small examination room has become a conditioned stimulus (CS) that has been associated with the drug injection and now elicits a conditioned response (CR) of an increased heart rate. This means that just the sight or thought of the examination room triggers the same physiological response as the drug itself.

This type of classical conditioning can have both positive and negative effects. On one hand, it can be beneficial for patients who are receiving treatment, as it can help them to anticipate and prepare for the effects of the drug.

On the other hand, it can also lead to a heightened anxiety or fear response in patients who may associate the examination room with negative experiences.

In summary, the repeated association of the drug injection with the small examination room has led to classical conditioning, resulting in an increased heart rate response to just being in the room.

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A Helmholtz resonator is essentially an acoustic device that consists of a cavity (usually a cylinder or sphere) with a small neck or opening.

The cavity is typically filled with air, and when sound waves enter the resonator, they cause the air inside the cavity to vibrate at specific resonant frequencies. These frequencies are determined by the size and shape of the cavity, as well as the size and shape of the neck or opening.

One of the key features of a Helmholtz resonator is its ability to suppress most frequencies while strongly amplifying a few specific resonant frequencies.

This is because the resonator acts as a filter, allowing only certain frequencies to pass through the neck or opening and enter the cavity. Any other frequencies are reflected or absorbed by the resonator, resulting in a reduction in overall sound levels.

Helmholtz resonators are commonly used in a variety of applications, such as in acoustic engineering to reduce noise levels in buildings or vehicles, in musical instruments to enhance specific frequencies, and in scientific experiments to study the properties of sound waves.

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The minimum horizontal force required to cause the lower block to slide out from under the upper block is F = μs(Mg + mg)

Let's consider the forces acting on the lower block. The weight of the block is mg, where g is the acceleration due to gravity. The normal force acting on the block is N = Mg + mg, where M is the mass of the upper block. The maximum static frictional force that can act between the two blocks is μsN.

If the applied force is F, the net force acting on the lower block is F - μsN. If this net force is greater than zero, the block will slide. Therefore, we can write:

F - μsN > 0

Substituting for N, we get:

F - μs(Mg + mg) > 0

Solving for F, we get:

F > μs(Mg + mg)

Therefore, the minimum horizontal force required to cause the lower block to slide out from under the upper block isF = μs(Mg + mg).

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The height of the first floor is 7.5 meters if the water pressure on the ground is 50000 pa and 20,000 pa at the first floor.

Using the hydrostatic pressure equation, we can get the reference level as the water pressure at the ground floor:

P = ρgh

P is equal to 50000 Pa on the ground floor and 20000 Pa on the first. Water's constant density allows us to write:

P1/P2 = h1/h2

where P1 and h1 represent the ground floor pressure and height and P2 and h2 represent the first floor pressure and height.

Inputting the values provided yields:

50000/20000 = h1/h2

As a result, the first level is 2.5 times as tall as the bottom floor. The height of the first floor would be as follows if we used a typical height of 3 meters per storey:

2.5 × 3 = 7.5 meters for h2.

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The ISS maintains equilibrium using thrusters, gyroscopes, and aerodynamically stable components.

The International Space Station (ISS) maintains equilibrium in spite of unbalanced forces through the use of thrusters and gyroscopes. The thrusters can be fired in short bursts to adjust the station's position, while gyroscopes help to maintain its orientation in space.

The station's position and orientation are constantly monitored by ground control, which can send commands to adjust the thrusters and gyroscopes as needed to make equilibrium.

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The angle from the center of the Airy disk to the first dark ring is 0.0363 degrees, and the distance between the center of the disk and the first dark ring on a screen 2 meters away from the aperture is: 1.268 mm.

a. To find the angle from the center of the Airy disk to the first dark ring, we will use the formula sin(p) = (wavelength) / (aperture diameter). Plugging in the values, we get sin(p) = 632.8 * 10^-9 / 0.001. Then, we calculate the inverse sine, sin^-1(0.0006328) = 0.0363 degrees.

b. To determine the distance between the center of the Airy disk and the first dark ring on a screen that is 2 meters from the aperture, we will use the formula distance = (angle) * (distance to screen).

In this case, distance = 0.0363 degrees * 2 meters.

First, convert the angle to radians: 0.0363 degrees * (pi / 180) = 0.000634 radians.

Then, multiply by the distance to the screen: 0.000634 radians * 2 meters = 0.001268 meters or 1.268 mm.

In summary, the angle from the center of the Airy disk to the first dark ring is 0.0363 degrees, and the distance between the center of the disk and the first dark ring on a screen 2 meters away from the aperture is 1.268 mm.

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Complete question:

A laser beam is aimed through a circular aperture of diameter 1 mm.

a. If the laser beam is red with a wavelength of 632. 8 nm, what is the angle from the center of the Airy disk to the first dark ring? (2 points)

sin(p) = 632. 8*10^-9 /. 001

sin^-1(. 0006328) =. 0363 degrees

b. If the screen you are projecting the Airy disk onto is 2 m from the aperture, what is the distance between the center of the disk and the first dark ring? (2 points)

The minimum runway length required for this airplane to reach the required speed for takeoff is 193.41 meters.

(a) To determine if the airplane can reach the required speed for takeoff on a 150m long runway, we can use the equation: v^2 = u^2 + 2as. Here, v is the final speed (27.8 m/s), u is the initial speed (0 m/s, assuming the plane starts from rest), a is the acceleration (2.00 m/s^2), and s is the distance (150m).

27.8^2 = 0^2 + 2(2.00)(150)
773.64 = 600

Since 773.64 > 600, this airplane cannot reach the required speed for takeoff on a 150m long runway.

(b) To find the minimum runway length required for this airplane to take off, we can rearrange the equation: s = (v^2 - u^2) / 2a.

s = (27.8^2 - 0^2) / (2 * 2.00)
s = 773.64 / 4
s = 193.41m

So, the minimum runway length required for this airplane to reach the required speed for takeoff is 193.41 meters.

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The speed at which the ball hit the ground is 31.36 m/s.

Speed is the rate of change of distance.

To calculate the speed at which the ball hit the ground, we use the formula below

Formula:

Where:

From the question,

Given:

Substituite these values into equation 1

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12.7 ms−1 is the velocity of the glider

Define velocity.

When an object is moving, its velocity is the rate at which it is changing position as seen from a specific point of view and as measured by a specific unit of time.

Velocity can be defined as the rate at which something moves in a specific direction. as the speed of a car driving north on a highway or the speed at which a rocket takes off.

Given,

Horizontal speed ∣→vh∣ =12.5 ms−1

t=Distance/Speed ⇒

t=6.00/12.5= 0.48s

Vertical speed

∣→vv∣=1.00/0.48=2.083 ms−1

∣→v∣=√(12.52)+(2.083)2

      = 12.7 ms−1

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