Ferdinand the frog is hopping from lily pad to lily pad in search of a good fly
for lunch. If the lily pads are spaced 2.4 m apart, and Ferdinand jumps with a
speed of 5.4m/s, taking 0.60 s to go from lily pad to lily pad, at what angle
must Ferdinand make each of his jumps?

Answer:

  68.79 N, 13.84° N of W

Explanation:

The law of cosines can be used to find the magnitude of the sum. F1 is 30° N of W, and F2 is 30° S of W, so the exterior angle of the force triangle is 30°+20° = 50°. The interior angle is the supplement of that. The angle between F1 and F2 in the force triangle representing the sum is 130°, so the sum of forces is ...

  |F|^2 = |F1|^2 +|F2|^2 -2·|F1|·|F2|·cos(130°)

  = 50^2 +25^2 -2·50·25·cos(130°) ≈ 4731.969

  |F| ≈ √4731.969 ≈ 68.79 . . . . newtons

The angle α between F and F1 can be found from the law of sines.

  sin(α)/|F2| = sin(130°)/|F|

  α = arcsin(|F2|/|F|·sin(130°)) ≈ 16.16°

The diagram shows this to be the angle south of F1, so the angle of the sum vector F is 30° -16.16° N of W = 13.84° N of W.

The resultant force vector is 68.79 N at an angle of 13.84° N of W.

Answer:

68.98N, 13.8° N of W

Explanation:

The Forces F1+ F2 = 50N 30°N of W + 25N 20°S of W.

This forces can be split into horizontal and vertical components and are sum as such.

The horizontal and vertical component of F1 are;

50N cos 30= 43.30N W

50N sin 30 = 25N

The horizontal and vertical component of F2 are;

25N cos20°=23.49N West

25N sin20°=8.55N South

Sum of horizontal forces =43.30N+23.49 = 66.99N

Sum of vertical forces =25-8.55=16.45N{North is at the positive side of the y axis and South at the negative side}

The resultant sum of this forces is √(66.99)^2 + (16.45)^2=√4758.26=68.98N

The angle at which this force moves is Tan^{-1} 16.45/66.99 = 13.8° N of W

The Force therefore is 68.98N, 13.8° N of W

The car that has the greater acceleration magnitude is car B

Torricelli's theorem can be used to calculate the magnitude of an object's acceleration when the value of time is not known:

                                            \(v^{2} = v_{0}^{2} + 2a\Delta S\)

Note that \(v\\\) is the final velocity value, \(v_{0}\) is the initial velocity value, \(a\) is the acceleration value, and \(\Delta S\) is the displacement.

Substituting the values ​​given by the question in the formula, we have:

                                           \(10^{2}= 0^{2}+2\times a \times 50\)

                                                    \(100 = 100a\)

                                                     \(a = 1m/s^{2}\)

    2. CAR B

                                               \(20^{2} = 10^{2} + 2\times a \times 50\)

                                                   \(400 = 100 + 100a\)

                                                        \(100a=300\)

                                                         \(a = 3m/s^{2}\)

So, comparing the two acceleration calculated above,  it is assumed that the car has the greater acceleration magnitude is car B with \(3m/s^{2}\)  comparing to \(1m/s^{2}\)  of the car A.

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Answer:

1.696 nm

Explanation:

For a diffraction grating, dsinθ = mλ where d = number of lines per metre of grating = 5510 lines per cm = 551000 lines per metre and λ = wavelength of light = 467 nm = 467 × 10⁻⁹ m. For a principal maximum, m = 1. So,

dsinθ = mλ = (1)λ = λ

dsinθ = λ

sinθ = λ/d.

Also tanθ = w/D where w = distance of center of screen to principal maximum and D = distance of grating to screen = 1.03 m

From trig ratios 1 + cot²θ = cosec²θ

1 + (1/tan²θ) = 1/(sin²θ)

substituting the values of sinθ and tanθ we have

1 + (D/w)² = (d/λ)²

(D/w)² = (d/λ)² - 1

(w/D)² = 1/[(d/λ)² - 1]

(w/D) = 1/√[(d/λ)² - 1]

w = D/√[(d/λ)² - 1] = 1.03 m/√[(551000/467 × 10⁻⁹ )² - 1] = 1.03 m/√[(1179.87 × 10⁹ )² - 1] = 1.03 m/1179.87 × 10⁹  = 0.000848 × 10⁻⁹ = 0.848 × 10⁻¹² m = 0.848 nm.

w is also the distance from the center to the other principal maximum on the other side.

So for both principal maxima to be on the screen, its minimum width must be 2w = 2 × 0.848 nm = 1.696 nm

So, the minimum width of the screen must be 1.696 nm

Answer:

B = 0.8 T

Explanation:

It is given that,

Radius of circular loop, r = 0.75 m

Current in the loop, I = 3 A

The loop may be rotated about an axis that passes through the center and lies in the plane of the loop.

When the orientation of the normal to the loop with respect to the direction of the magnetic field is 25°, the torque on the coil is 1.8 Nm.

We need to find the magnitude of the uniform magnetic field exerting this torque on the loop. Torque acting on the loop is given by :

\(\tau=NIAB\sin\theta\)

B is magnetic field

\(B=\dfrac{\tau}{NIA\sin\theta}\\\\B=\dfrac{1.8}{1\times \pi \times (0.75)^2\times 3\times \sin(25)}\\\\B=0.8\ T\)

So, the magnitude of the uniform magnetic field exerting this torque on the loop is 0.8 T.

On one cookie containing 50 calories, you could potentially go approximately 298 meters

Given that one food calorie is equivalent to 4184 joules, we can calculate the total energy in joules contained in the 50 calorie cookie:

50 food calories * 4184 J/calorie = 209,200 joules

Assuming an average efficiency of around 25% (meaning 25% of the energy is effectively used for movement), and a body weight of 70 kilograms, we can use a rough estimation that it takes about 1 joule of energy to move 0.4 meters (based on the energy cost of walking).

Distance = (Energy obtained from the cookie * Efficiency) / (Energy cost per meter * Body weight)

Distance = (209,200 J * 0.25) / (1 J/m * 0.4 m/kg * 70 kg)

Distance ≈ 298 meters

Therefore, on one cookie containing 50 calories, you could potentially go approximately 298 meters

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The answer is B) I. The electric field will have the greatest magnitude at point I because it is the closest point to the charged conductors. The closer to the conductors, the greater the electric field magnitude.

Electric field is an invisible force field that surrounds any object that has an electric charge. It is measured in terms of volts per meter (V/m) and is responsible for the attraction or repulsion of two objects with different electric charges. The force of the electric field is determined by the amount of charge on the objects and the distance between them. Any changes in the electric field will cause a corresponding change in the force felt by the objects. Electric fields can be created by moving charges, such as those found in electric currents, or by static charges, such as those found on a charged object. Electric fields are essential for the transmission of electrical signals and are used in many applications, from telecommunications to medical imaging.

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The magnetic field that forms when a wire carries an electric current is a circular field that is strongest at the ends of the wire and weakest in the middle.

A current-carrying wire's magnetic field looks like a series of concentric circles that extend outward from the wire in both directions.

The magnitude of the magnetic field is greatest at the center of the wire and decreases as you move away from it.

The direction of the magnetic field is determined by the direction of the current flow: if the current is flowing clockwise around the wire, then the magnetic field will be pointing outward from the wire.

The magnetic field also has a north and south pole, so the direction of the field also depends on which direction around the wire the current is flowing.

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Answer:

The tissue that holds bones together at movable joints is ligaments. Ligaments are strong, fibrous connective tissues that connect bones to other bones, providing stability and limiting excessive movement at the joints. They help to maintain the proper alignment and function of the joints while allowing for controlled movement.

Explanation:

The tissue that holds bones together at movable joints is ligaments. Ligaments are strong, fibrous connective tissues that connect bones to other bones, providing stability and limiting excessive movement at the joints. They help to maintain the proper alignment and function of the joints while allowing for controlled movement.

Answer:

The answer is ligaments!

Explanation:

Hope this helps!! :)

The total resistance of the circuit is 49 Ω. The current strength in the circuit, when connected to a voltage source of 56 V, is approximately 1.14 A.

To calculate the total resistance of the circuit, we need to determine the equivalent resistance of the resistors connected in a series.

Given:

R1 = 4 Ω

R2 = 30 Ω

R3 = 10 Ω

R4 = 5 Ω

Calculate the equivalent resistance (RT) of R1 and R2, as they are connected in series:

RT1-2 = R1 + R2

RT1-2 = 4 Ω + 30 Ω

RT1-2 = 34 Ω

Calculate the equivalent resistance (RTotal) of RT1-2 and R3, as they are connected in parallel:

1/RTotal = 1/RT1-2 + 1/R3

1/RTotal = 1/34 Ω + 1/10 Ω

1/RTotal = (10 + 34) / (34 * 10) Ω

1/RTotal = 44 / 340 Ω

1/RTotal ≈ 0.1294 Ω

RTotal ≈ 1 / 0.1294 Ω

RTotal ≈ 7.74 Ω

Calculate the equivalent resistance (RTotalCircuit) of RTotal and R4, as they are connected in series:

RTotalCircuit = RTotal + R4

RTotalCircuit = 7.74 Ω + 5 Ω

RTotalCircuit ≈ 12.74 Ω

Therefore, the total resistance of the circuit is approximately 12.74 Ω.

To determine the current strength (I) when connected to a voltage source of 56 V, we can use Ohm's Law:

I = V / RTotalCircuit

I = 56 V / 12.74 Ω

I ≈ 4.39 A

Therefore, the current strength in the circuit, when connected to a voltage source of 56 V, is approximately 4.39 A (or 1.14 A, considering significant figures).

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Answer:

D. Gas

Explanation:

There are only three states of matter: solid, liquid and gas. This makes choice c (Mixture) incorrect because it is not part of the group.

The particles in gas are widely separated, which means there's a lot of free space between the particles. This makes it easily compressible. The particles then move past each other, which causes no regular arrangement.

As a result, the picture behind the mirror is virtual, upright, and enlarged.

You will find that the properties of an image (SALT) created in a concave mirror depend on the object's position. A) if the item is larger than C. Size, attitude, and location are all important considerations.

The image will be true, but reversed and much reduced. To obtain a crisp flame image, move the burning candle towards the mirror while moving the screen away from it. The size of the inverted picture grows.

Concave mirrors may create both physical and virtual images. A virtual and enlarged picture is produced when the item gets closer to the mirror. When the item is placed further away from the mirror,.

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equal in magnitude but opposite in direction

The statement that is true about momentum is as follows: Momentum is a vector (option D).

Momentum is the tendency of a body to maintain its inertial motion. It is the product of its mass and velocity, or the vector sum of the products of its masses and velocities.

Momentum is a vector quantity i.e. it has both magnitude and direction.

Since momentum is a product of mass and velocity, it's S.I unit is kgm/s or N/s.

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Momentum is that momentum is a vector quantity. Therefore, the answer is option D.Momentum is a property of objects that are moving, that is, an object's tendency to stay in motion. Momentum is a measure of an object's motion or its inertia in motion.

An object's momentum is calculated as the product of its mass and its velocity, with the direction of momentum being the same as the direction of velocity.Vector and scalar quantitiesMomentum is a vector quantity because it has both magnitude and direction. A scalar quantity, on the other hand, is a quantity that has only magnitude and no direction.

For example, speed is a scalar quantity because it is defined as distance divided by time and has only magnitude (no direction).In physics, there are two types of quantities: vector quantities and scalar quantities. A vector quantity is a quantity that has both magnitude and direction, whereas a scalar quantity is a quantity that has only magnitude.

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Given:

The diameter of the circular loop is: d = 2r = 21.475 cm.

The current in the wire is: I = 3.917 A.

To find:

The magnetic field at the center of the loop.

Explanation:

The magnetic field at the center of the circular loop is:

Final answer:

The magnetic field at the center of the circular loop is 22.92 micro Tesla.

Answer:

3.39 rad / s.

Explanation:

Given data:

mass of disk = 4.50 Kg

radius of wheel = 0.650 m

mass of the clay = 0.870 kg

The moment of inertial of the wheel = I = 4.5 kg x ( 0.65 m )2 / 2 = 0.95 kg . m2.

Now, applying the principle of angular momentum conservation :

Iω_i = ( I + mr2 )ω_f.

where ω_i = initial angular speed= 4.70 rad/s, ω_f = final angular speed

Hence, ω_f = Iω_i / ( I + mr2 )

= ( 0.95 kg . m2 x 4.7 rad / s ) / [ 0.95 kg . m2 + 0.87 kg x ( 0.65 m )2 ]

= 3.39 rad / s.

Hence, correct answer is  : 3.39 rad / s.

Answer:

Explanation:

Quarter 1 - 10,000 units

Quarter 2 - 12,000 units

Quarter 3 - 16,000 units

Quarter 4 - 14,000 units

Quarter 5 - 10,000 units

Quarter 6 - 8,000 units

Based on this information, the total estimated sales revenue for the next six quarters is Br. 480,000.

Answer:

speed

Explanation:

Lower frequencies (red) move faster in a glass prism than higher frequencies.

Light of all colors moves at the same speed in a vacuum. However, light travels at different speeds in many media, including water.

Red light moves through glass at the fastest speed, whereas violet light moves at the slowest speed.

Red light bends the least of all the colors because it moves at the fastest speed, whereas violet light moves at the slowest speed and bends the most.

Wavelength and speed are directly proportional. Speed also rises with increasing wavelength. Light that has a maximal wavelength therefore moves at its fastest.

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Answer:

a. If the frequency of light is increased above the threshold frequency, the energy of the electrons emitted will increase.

b. If the frequency of light is decreased to below the threshold frequency, the rate at which electrons are emitted will decrease.

c. If the intensity of light is decreased, the energy of the electrons emitted will remain the same, but fewer electrons will be emitted.

d. If the intensity of light is decreased, the rate at which electrons are emitted will decrease.

A rope pulls a Tesla out of mud. The guy pulls a force F⊥ of 300N, and theta = 4.2°. The tension force T is 298.44__ Newton.

The problem describes a Tesla that is stuck in the mud and needs to be pulled out using a rope. the guy pulls a force F⊥ of 300N and that the angle between the rope and the horizontal plane is θ = 4.2°. The goal is to find the tension force T exerted by the rope.To solve for T, we'll need to use trigonometry. We can break the force vector into its horizontal and vertical components as follows:

Fx = F⊥ cosθ and Fy = F⊥ sinθ.

Since the rope is pulling the Tesla horizontally, the horizontal component of the force will be the tension force T. So we have:

T = Fx = F⊥ cosθ = (300 N) cos(4.2°) ≈ 298.44 N

Taking the cosine of the angle is necessary since it's the adjacent side that we're interested in, which is the horizontal component of the force. Therefore, the tension force exerted by the rope is approximately 298.44 N.

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We have that the  the strength of the force between the Sun and the moon  is mathematically given as

F2=0.12140F1N

Question Parameters:

Distance between the Earth and the Sun were increased by a factor of 2.87,

Generally the equation for the  Gravitational Force   is mathematically given as

\(F=\frac{Gm1m2}{d^2}\\\\Where\\\\f1/f2=d1^2/d2^2\\\\Therefore\\\\F2=\frac{F1*d1}{3.23^2}\\\\F2=\frac{F1*1}{2.87^2}\\\\\)

F2=0.12140F1N

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Answer:

Yes, it would make it back up.

Explanation:

If it has 100,000 Joules of gravitational potential energy at the top of the hill, by the time the cart gets to the bottom, it will become PE = 0, KE = 90,000 since 10% of 100,000 is 10,000. The cart only requires 80,000J to climb back up so it should easily do so.

I didn't quite understand if the 10% energy loss is total, or every time it goes up or down, but it isn't a problem because 10% of 90,000 is 9,000, which means it would have 81,000J of energy on the way back up IF it loses energy due to friction on the way back up also.

The only physical law you need to prove this is the Law of Conservation of Energy: no energy is lost, only transformed; 10% of the energy becomes heat, the rest remains mechanical energy, which is the reason why the reasoning above works.

projectile's vertical speed v yv y v, start , y,  drops prior to reaching its maximum height since its acceleration is in the opposite direction. Since the object's height is rising, the initial direction of the velocity is upward

.

At the projectile's highest point, vertical velocity zeroes out. After reaching the highest point, the vertical speed increases due of the same-direction acceleration. As the object's height lowers, the vertical velocity has a downward direction.

In projectile The beginning vertical velocity determines the maximum height. Increasing the launch angle raises the maximum height because steeper launch angles have a larger vertical velocity component.

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If the point M(0,38) is on the circle then its radio is:

\(r = \sqrt{ 0 ^2+38 ^2} = 38\)

Compute the distance between the center and N:

\(d = \sqrt{(-5)^2 + (-3)^2} = \sqrt{25+9} = \sqrt{34} \approx 5.83\)

Because d < r then point N is INSIDE THE CIRCLE.

Answer:

Instrument Use

Accelerometer Measures acceleration

Altimeter Measures altitude of an aircraft

Ammeter Measures electric current in ampere

Anemometer Measures wind speed

Answer:

C. Fill two identical pots with equal volumes of salt water and tap water and use a stopwatch to determine the time it takes each pot to boil.

Explanation:

A) is incorrect because Peter should have the same testing environment for both of his experiments.

He should choose the same method of boiling the salt water and tap water because the stovetop and the microwave could also affect the results and make them unreliable.

B) is incorrect because Peter should not estimate the time it takes the salt water and tap water to boil.

Peter should measure and record the amount of time that it takes these substances to boil in order to have an accurate, valid experimental thesis.

C) is correct because Peter uses the same volume of salt water and tap water, fills them into two identical pots, and uses a stopwatch to determine the amount of time it takes each pot to boil.

The stopwatch makes the experiment more valid and accurate compared to the previous methods, and the identical pots and amounts of water help this experiment become even more precise.

D) is incorrect because the variables in the experiment are not controlled amounts and will therefore produce an inaccurate and invalid experiment.

To calculate the torque required to create an angular acceleration, we can use the formula:

Torque = Moment of Inertia × Angular Acceleration

The moment of inertia of a disk can be calculated using the formula:

Moment of Inertia = (1/2) × Mass × Radius^2

Given:

Mass = 15,000 kg

Radius = 6.14 m

Angular Acceleration = 0.0500 rad/s^2

First, calculate the moment of inertia:

Moment of Inertia = (1/2) × Mass × Radius^2

Moment of Inertia = (1/2) × 15,000 kg × (6.14 m)^2

Next, calculate the torque:

Torque = Moment of Inertia × Angular Acceleration

Torque = Moment of Inertia × 0.0500 rad/s^2

Now, let's plug in the values and calculate:

Moment of Inertia = (1/2) × 15,000 kg × (6.14 m)^2

Moment of Inertia ≈ 283,594.13 kg·m^2

Torque = 283,594.13 kg·m^2 × 0.0500 rad/s^2

Torque ≈ 14,179.71 N·m

Rounding to three significant figures, the torque required to create an angular acceleration of 0.0500 rad/s^2 is approximately 14,180 N·m.

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All the equations of motion are as follows, Displacement (s) equation, Final velocity (v) equation, Average velocity (v_avg) equation, Displacement (s) equation with average velocity, and Displacement (s) equation.

In terms of its motion as a function of time, equations of motion define how a physical system behaves. In more detail, the equations of motion define how a physical system behaves as a collection of mathematical functions expressed in terms of dynamic variables.

In conclusion, equations of motion define how a physical system behaves in terms of how its motion changes over time.

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