A boy who exerts a 300-N force on the ice of a skating rink is pulled by his friend with a force of 75 N, causing the boy to accelerate across the ice. If drag and the friction from the ice apply a force of 5 N on the boy, what is the magnitude of the net force acting on him?

Answers

Answer 1

Answer:

70 N

Explanation:

Draw a free body diagram of the boy.  There are four forces:

Weight force mg pulling down,

A 300 N normal force pushing up,

A 75 N applied force pulling right,

and a 5 N friction force pushing left.

The boy's acceleration in the y direction is 0, so the net force in the y direction is 0.

The net force in the x direction is 75 N − 5 N = 70 N.


Related Questions

Multiply the number 4.48E-8 by 5.2E-4 using Google. What is the correct answer in scientific notation?

Answers

Answer:

[tex]2.32\times 10^{-11}[/tex]

Explanation:

First number is [tex]4.48\times 10^{-8}[/tex]

Second number is [tex]5.2\times 10^{-4}[/tex]

We need to multiply the two numbers.

[tex]4.48\times 10^{-8}\times 5.2\times 10^{-4}=(4.48\times 5.2)\times 10^{(-8-4)}\\\\=23.296\times 10^{-12}[/tex]

In scientific notation : [tex]2.32\times 10^{-11}[/tex]

Hence, this is the required solution.

Assume that Earth is in circular orbit around the Sun with kinetic energy K and potential energy U, taken to be zero for infinite separation. Then, the relationship between K and U:

Answers

Answer:

K= -U/2

Explanation:

We know that K.E = 1/2mv²

And -GMm/r²= mv²/r

Thus K,E= 1/2(GMm/r)= 1/2(-P.E)

So

P.E = - GMm/r

So K= -U/2


A postal service worker lifts a package into a truck. She exerts 22 J of work lifting the package for 4 seconds. How much power did she user

Answers

Given:-

Work done = 22 Joules

Time taken = 4 Seconds

To be calculated:-

Calculate the power .

Formula used:-

Power = Work done/Time taken

Solution:-

We know that,

[tex] \sf{Power = \dfrac{Work \: done}{Time \: taken } }[/tex]

★ Putting the values in the above formula,we get:

[tex] \sf{Power = \dfrac{22}{4} }[/tex]

[tex] \sf{Power = 5.5 \: watts}[/tex]

In a compound microscope, the objective has a focal length of 1.0 cm, the eyepiece has a focal length of 2.0 cm, and the tube length is 25 cm. What is the magnitude of the overall magnification of the microscope?

Answers

Answer:

The  value  is   [tex]m \approx 310[/tex]

Explanation:

From the question we are told that

     The  focal length of the objective is  [tex]f_o = 1.0 \ cm[/tex]

    The  focal length of the eyepiece is  [tex]f_e = 2.0 \ cm[/tex]

    The  tube length is  [tex]L = 25 \ cm[/tex]

Generally the magnitude of the overall magnification is mathematically represented as

            [tex]m = m_o * m_e[/tex]

Where  [tex]m_o[/tex] is the objective magnification which is mathematically represented as

        [tex]m_o = \frac{L}{f_o }[/tex]

=>      [tex]m_o = \frac{25}{1 }[/tex]

=>      [tex]m_o = 25[/tex]

[tex]m_e[/tex] is the eyepiece magnification which is mathematically evaluated as

     [tex]m_e = \frac{L }{f_e }[/tex]

     [tex]m_e = \frac{25 }{ 2}[/tex]

      [tex]m_e = 12.5 \ cm[/tex]

So

    [tex]m = 25 * 12.5[/tex]

     [tex]m \approx 310[/tex]

a telescope is oriting on a spacecraft aroudn the earth. Speed of 3.25 x 10^5 mass 7500 kg. What is the de Broglie wavelength of the telescope. g

Answers

Answer:

2.72 x 10^-43 m

Explanation:

mass of the telescope = 7500 kg

speed of the telescope = 3.25 x 10^5 m/s

de Broglie's  wavelength of the telescope is given as

λ = h/mv

where

λ is the wavelength of the telescope

h is the plank's constant = 6.63 × 10-34 m^2 kg/s

m is the mass of the telescope = 7500 kg

v is speed of the telescope = 3.25 x 10^5 m/s

substituting value, we have

λ = (6.63 × 10-34)/(7500 x 3.25 x 10^5)

λ = 2.72 x 10^-43 m

Select all the statements that are true about the dependent variable.
a. It is also the "then" part of your hypothesis.
b. It's sometimes called the "responding variable"
c. It always stays the same.
d. It's often abbreviated as "DV"

Answers

Answer:

Hey there!

These are true:

a. It is also the "then" part of your hypothesis.

b. It's sometimes called the "responding variable"

d. It's often abbreviated as "DV"

Let me know if this helps :)

You are performing a double slit experiment very similar to the one from DL by shining a laser on two nattow slits spaced 7.5 x 103 meters apart. However, by placing a piece of crystal in one of the slits, you are able to make it so that the rays of light that travel through the two slits are Ï out of phase with each other (that is to say, Ao,- ). If you observe that on a screen placed 4 meters from the two slits that the distance between the bright spot clos center of the pattern is 1.5 cm, what is the wavelength of the laser?

Answers

Complete Question

You are performing a double slit experiment very similar to the one from DL by shining a laser on two nattow slits spaced [tex]7.5 * 10^{-3}[/tex] meters apart. However, by placing a piece of crystal in one of the slits, you are able to make it so that the rays of light that travel through the two slits are Ï out of phase with each other (that is to say, Ao,- ). If you observe that on a screen placed 4 meters from the two slits that the distance between the bright spot closest to center of the pattern is 1.5 cm, what is the wavelength of the laser?

Answer:

The  wavelength is  [tex]\lambda = 56250 nm[/tex]

Explanation:

From the question we are told that

   The  distance of slit separation is  [tex]d = 7.5 *10^{-3} \ m[/tex]

   The  distance of the screen is  [tex]D = 4 \ m[/tex]

    The  distance between the bright spot closest to the center of the interference  is  [tex]k = 1.5 \ cm = 0.015 \ m[/tex]

   

Generally the width of the central  maximum fringe produced is mathematically represented as

        [tex]y = 2 * k = \frac{ D * \lambda}{d}[/tex]

  =>    [tex]2 * 0.015 = \frac{ \lambda * 4}{ 7.5 *10^{-3}}[/tex]

   =>   [tex]\lambda = 56250 *10^{-9} \ m[/tex]

=>      [tex]\lambda = 56250 nm[/tex]

Which contains the most moles: 10 g of hydrogen gas, 100 g of carbon, or 50 g of lead?

Answers

Answer:

Carbon

Explanation:

We know that

Number of moles = mass/molecular mass

So

Hydrogen: given as H2 with 10g an atomic number of 1 so MW( 1x 2= 2)

Number of moles = Weight/MW

= 10/2

= 5

Carbon: atomic number 12 C and mass 100

Number of moles = Weight/MW

= 100/12

= 8.33

Lead: atomic num 207 and mW 207 pb

Number of moles = Weight/MW

= 50/207

= 0.241

Therefore Carbon has the most moles.

A car traveling at 10 m/s passes over a hill on a road that has a circular cross section of radius 30 m. What is the force exerted by the seat of the car on a 60-kg passenger when the car is passing the top of the hill?

Answers

Answer:

F= 389N

Explanation:

Using

Mg-N=mv²/ r

So N= mg- mv²/r

60*9.8- 60*10²/30

=389N

Describe an experiment to show that the pressure in a liquid increases with depth.

Answers

Answer:

Explanation:

Water pressure is the result of the weight of all the water above pushing down on the water below. As you go deeper into a body of water, there is more water above, and therefore a greater weight pushing down. This is the reason water pressure increases with depth.

A force of 200 N is applied on small piston of a pascal press. What would be the
force applied on the big piston, if the diameter of the small piston is 4.37 cm and the area of the big piston is 98 cm2?

Answers

Answer:

The force applied on the big piston is 1306.67 N

Explanation:

Given;

force applied on small piston, F₁ = 200 N

diameter of the small piston, d₁ = 4.37 cm

radius of the small piston, r₁ = d₁/2 = 2.185 cm

Area of the small piston, A₁ = πr₁² = π(2.185 cm)² = 15 cm²

Area of the big piston, A₂ = 98 cm²

The pressure of the piston is given by;

[tex]P = \frac{F}{A} \\\\\frac{F_1}{A_1} = \frac{F_2}{A_2}\\\\ F_2 = \frac{F_1A_2}{A_1}[/tex]

Where;

F₂ is the force on big piston

[tex]F_2 = \frac{200*98}{15} \\\\F_2 = 1306.67 \ N[/tex]

Therefore, the force applied on the big piston is 1306.67 N

If a single circular loop of wire carries a current of 61 A and produces a magnetic field at its center with a magnitude of 1.70 10-4 T, determine the radius of the loop.

Answers

Answer:

The  radius is  [tex]R = 0.22 5 \ m[/tex]

Explanation:

From the question we are told that

    The current is  [tex]I = 61 \ A[/tex]

     The  magnetic field is  [tex]B = 1.70 *10^{-4} \ T[/tex]

Generally the magnetic field produced by a current carrying conductor  is mathematically represented as

        [tex]B = \frac{\mu_o * I}{2 * R }[/tex]

=>     [tex]R = \frac{\mu_o * I }{ 2 * B }[/tex]

Here  [tex]\mu_o[/tex] is the permeability of free space with value  [tex]\mu_o = 4\pi * 10^{-7} N/A^2[/tex]

=>    [tex]R = \frac{ 4\pi * 10^{-7} * 61 }{ 2 * 1.70 *10^{-4} }[/tex]

=>  [tex]R = 0.22 5 \ m[/tex]


If you have two substances, one with a density of 2.0 g/cm3 and one with a density of 1.3 g/cm3 and you combined them, which one would float on top
other and why?

Answers

Explanation:

Assuming the substances are fluids that do not mix, the lighter substance (ρ = 1.3 g/cm³) will float on top of the heavier substance (ρ = 2.0 g/cm³).  This is due to Archimedes' Principle, which explains buoyancy.

Which of the following statements about electromagnetic radiation is true?
A) It always travels at 3Ã108 m/s.
B) It consists of perpendicularly oscillating electric and magnetic fields, and the direction of propagation is perpendicular to both.
C) It consists of oscillating electric and magnetic fields that are parallel to one another and perpendicular to the direction of propagation.
D) The oscillating electric and magnetic fields are completely out of phase with one another

Answers

Answer:

The correct option is B: It consists of perpendicularly oscillating electric and magnetic fields, and the direction of propagation is perpendicular to both.

Explanation:

Electromagnetic radiation travels at the speed of light (c = 3x10⁸ m/s) only in a vacuum. In another propagation medium, the speed of electromagnetic radiation is less than c.    

The oscillations of the waves of the electric and magnetic fields are perpendicular to each other, and the direction of propagation is also perpendicular to the two fields.        

           

From all of the above, the correct option is B: It consists of perpendicularly oscillating electric and magnetic fields, and the direction of propagation is perpendicular to both.        

I hope it helps you!                              

The true statement regarding electromagnetic radiation should be option B where it comprises of perpendicularly oscillating electric and magnetic fields.

What is electromagnetic radiation?

It should be traveled when the speed of light i.e. (c = 3x10⁸ m/s) should be a vacuum. For the propagation medium, the speed with respect to the electromagnetic radiation should be lower than c. Also, the oscillations of  the electric waves and the magnetic field should be perpendicular also the direction should be perpendicular

Hence, the option b is correct.

Learn more about radiation here: https://brainly.com/question/24301101

A horizontal wire carries a current (conventional) straight toward you. From your point of view, the magnetic field caused by the current in the wire is doing what?

Answers

Answer:

The magnetic field circles the wire in a counter-clockwise direction.

Explanation:

This is by using Fleming right hand rule which says If you point your pointer finger in the direction the positive charge is moving, and then your middle finger in the direction of the magnetic field, your thumb points in the direction of the magnetic force pushing on the moving charge.

In a ballistics test, a 24 g bullet traveling horizontally at 1200 m/s goes through a 31-cm-thick 320 kg stationary target and emerges with a speed of 910 m/s. The target is free to slide on a smooth horizontal surface. What is the targetâs speed just after the bullet emerges?

Answers

Answer:

The  velocity is  [tex]v_t = 0.02175 \ m/s[/tex]

Explanation:

From the question we are told that

   The  mass of the bullet is  [tex]m_b = 0.024 \ kg[/tex]

    The initial speed of the bullet is  [tex]u_b = 1200 \ m/s[/tex]

   The mass of the target is  [tex]m_t = 320 \ kg[/tex]

    The  initial velocity of target is  [tex]u_t = 0 \ m/s[/tex]

    The  final velocity of the bullet is  is  [tex]v_b = 910 \ m/s[/tex]

   

Generally according to the law of momentum conservation we have that

      [tex]m_b * u_b + m_t * u_t = m_b * v_b + m_t * v_t[/tex]

=>   [tex]0.024 * 1200 + 320 * 0 = 0.024 * 910 + 320 * v_t[/tex]

=>    [tex]v_t = 0.02175 \ m/s[/tex]

A 50 kg laboratory worker is exposed to 30 mJ of neutron radiation with an RBE of 10. Part A What is the dose in mSv

Answers

Answer:

The dose is 6 mSV

Explanation:

The absorbed dose (in gray - Gy) is the amount of energy that ionizing radiation deposits per unit mass of tissue. That is,

Absorbed dose = Energy deposited / Mass

while Dose equivalent (DE) (in Seivert -Sv) is given by

DE = Absorbed dose × RBE (Relative biological effectiveness)

First, we will determine the Absorbed dose

From the question, Energy deposited = 30mJ and Mass = 50kg

From,

Absorbed dose = Energy deposited / Mass

Absorbed dose = 30mJ/50kg

Absorbed dose = 0.6 mGy

Now, for the Dose equivalent (DE)

DE = Absorbed dose × RBE

From the question, RBE = 10

Hence,

DE = 0.6mGy × 10

DE = 6 mSv

The dose will be 6 mSv. The absorbed dose (in gray - Gy) is the amount of energy that ionizing radiation deposits per unit mass of tissue.

What is the dose?

A unit is a measurable quantity of a drug, vitamin, or pathogen provided in a single dose. A medication's dosage form is a blend of active and inactive ingredients used to give it.

The given devotion is;

[tex]D_a=[/tex]Absorbed dose

[tex]\rm E_D[/tex] = energy deposited

[tex]\rm D_E[/tex] is the dose equivalent

RBE= Relative biological effectiveness

The absorbed dose is found as;

[tex]\rm D_a = \frac{E_d}{m}\\\\ D_a = \frac{30 \ mJ}{50}\\\\ \rm D_a = 0.6 \ mGy[/tex]

The dose equivalent is found as;

[tex]\rm D_E=D_A \times RBE \\\\ D_E=0.6 \times 10 \\\\ \rm D_E=6 mSV[/tex]

Hence the dose will be 6 mSv.

To learn more about the dose refer to the link;

https://brainly.com/question/12971282

88. A child pulls a cart to the left along a rough surface. Which one of the free body diagrams correctly depicts all the forces acting on the carrito?

Answers

Answer:

Eje x

           fr- F = m a

eje y    

           N-W =0

Explanation:

Para este ejercicio, debemos usar la segunda ley de Newton, donde se necesita fija un sistema de referencia el mas usado es un sistema horizontal y vertical para los ejes x e y  

en el adjunto puede ver el diagrama de cuerpo libre correcto,  

las fuerza son

Eje x

           fr- F = m a

eje y    

           N-W =0

la ecuacion para la fuerza de roce es

          fr = my N

A radio wave transmits 34.5 W/m2 of power per unit area. A flat surface of area A is perpendicular to the direction of propagation of the wave. Assuming the surface is a perfect absorber, calculate the radiation pressure on it.

Answers

Answer:

1.15*10^-7 N/m²

Explanation:

Radiation pressure is the pressure exerted on any surface, as a result of the exchange of momentum between the object and its electromagnetic field.

The formula to calculate radiation pressure on a perfect absorber is

P = s/c, where

P = radiation pressure

s = intensity of light

c = speed of light

Now, on substituting the values and plugging it into the equation, we have

P = 34.5 / 3*10^8

P = 1.15*10^-7 N/m²

therefore, radiation pressure is found to be 1.15*10^-7 N/m²

Waves on a String: The speed of sound in steel is 5000 m/s. What is the wavelength of a sound wave of frequency 660 Hz in steel

Answers

Answer:

The wavelength of the sound wave is 7.58 m

Explanation:

Given;

speed of wave in steel, v = 5000 m/s

frequency of the wave in steel, f = 660 Hz

The wavelength of a sound wave is given by;

λ = v / f

where;

v is the speed of sound wave in steel

f is the frequency of sound wave in steel

λ is the wavelength of the sound wave in steel

λ = 5000 / 660

λ = 7.58 m

Therefore, the wavelength of the sound wave is 7.58 m

blending three primary colors of light

Answers

Answer: white light

Explanation:

if you mix red and blue light together, you get magenta and when you mix blue and green light together, you get cyan and when you mix red and green light together, you get yellow but when you mix all three primary colors of light together, you end up with white light or as we see it.

Determine the centroid of the shaded area shown in figure 2. Determine the moment of inertia about y-axis of the shaded area shown in figure 2

Answers

Answer:

centroid: (x, y) = (81.25 mm, 137.5 mm)I = 8719.31 mm^2    for unit mass

Explanation:

Finding the desired measures requires we know a differential of area. That, in turn, requires we have a way to describe a differential of area. Here, we choose to use a vertical slice, which requires we know the area boundaries as a function of x.

The upper boundary is a line with a slope of 125/156.25 = 0.8, and a y-intercept of 125. That is, ...

  y1 = 0.8x +125

The lower boundary is given in terms of y, but we can solve for y to find ...

  100x = y^2

  y2 = 10√x

Then our differential of area is ...

  dA = (y1 -y2)dx

__

The centroid is found by computing the first moment about the x- and y-axes, and dividing those values by the area of the figure.

The area will be ...

  [tex]\displaystyle A=\int_0^{156.25}{dA}=\int_0^{156.25}{(y_1-y_2)}\,dx[/tex]

The y-coordinate of the centroid is ...

  [tex]\displaystyle \overline{y}=\dfrac{S_x}{A}=\dfrac{1}{A}\int_0^{156.25}{\dfrac{y_1+y_2}{2}}\,dA=\dfrac{1}{A}\int_0^{156.25}{\dfrac{y_1+y_2}{2}(y_1-y_2)}\,dx=137.5[/tex]

Similarly, the x-coordinate is ...

  [tex]\displaystyle \overline{x}=\dfrac{S_y}{A}=\dfrac{1}{A}\int_0^{156.25}{x}\,dA=\dfrac{1}{A}\int_0^{156.25}{x(y_1-y_2)}\,dx=81.25[/tex]

That is, centroid coordinates are (x, y) = (81.25, 137.5) mm.

__

The moment of inertia is the second moment of the area. If we normalize by the "mass" (area), then the integral looks a lot like the one for [tex]\overline{x}[/tex], but multiplies dA by x^2 instead of x.

The attachment shows that value to be ...

  I ≈ 8719.31 mm^2 (normalized by area)

The area is 16276.0416667 mm^2, if you want to "un-normalize" the moment of inertia.

What is the de Broglie wavelength of an electron that strikes the back of the face of a TV screen at 1 15 the speed of light

Answers

Answer:

Te wavelength is 3.66 x 10^-11 m

Explanation:

Question is

What is the de Broglie wavelength of an electron that strikes the back of the face of a TV screen at 1/15 the speed of light.

De Broglie's wavelength is gotten as

λ = h/mv

where

λ is the wavelength of the electron

h is the Planck's constant = 6.67 x 10^-34 J-s

m is the mass of an an electron = 9.109 x 10^-31 kg

v is the speed of the electron.

The speed of the electron is given as 1/15 of the speed of light

Speed of electron = 1/15 of 3 x 10^8 = 2.0 x 10^7 m/s

substituting values, we have

λ = (6.67 x 10^-34)/(9.109 x 10^-31)x(2.0 x 10^7) = 3.66 x 10^-11 m

Observe: Up until now, all the problems you have solved have involved converting only one unit. However, some conversion problems require you to convert two or more units. Select Speed from the menu. What two units do you need to convert to solve this problem? meter and seconds Think about it: How do you think you can use conversion factors to solve this problem?

Answers

Answer:

t is appropriate to clarify that units such as time and angles the transformation is not in base ten, for example:

        60 s = 1 min

        60 min = 1 h

        24 h = 1 day

Therefore, for this transformation, you must be more careful

the length transformation is base 10

Explanation:

In many exercises the units used are transformed by equations into other units called derivatives, in general the transformation of derived units is the product of the transformation of the constituent units.

In the example of velocity, the derivative unit is m / s, which is why it works in the same way that you transform length and time if in the equation it is multiplying it is multiplied and if it is dividing it is divided.

It is appropriate to clarify that units such as time and angles the transformation is not in base ten, for example:

        60 s = 1 min

        60 min = 1 h

        24 h = 1 day

Therefore, for this transformation, you must be more careful

the length transformation is base 10

      1000 m = 1 km

If the accuracy in measuring the position of a particle increases, the accuracy in measuring its velocity will

Answers

Answer:

Therefore the answer is the precision in the speed DECREASES

Explanation:

In quantum mechanics, we have the uncertainty principle that establishes that when the accuracy of the position increases the accuracy  the speed decreases, being related by the expression

               Δx Δv ≥  h'/ 2

                h' = h/2π

Therefore the answer is the precision in the speed DECREASES

A book sits on a bookshelf without moving until a student picks it up. Which law best explains why the book remains at rest until the student picks it up? (AKS 3a1 DOK 1) Newton's Second Law log Newton's Third Law Newton's Law of Universal Gravitation Newton's First Law​

Answers

Answer:

Newtons first law

Explanation:

object in rest stays at rest

object in motion stays in motion

A spaceship far from all other objects uses its impulse power system to attain a speed of 104 m/s. The crew then shuts off the power. According to Newton's first law, what will happen to the motion of the spaceship from then on

Answers

Answer:

The spaceship will travel in a straight line at constant speed.

Explanation:

According to the Newton's First Law, the spaceship will have an uniform motion in a straight line, that is, the spaceship will travel in a straight line at constant speed.

The spaceship will travel in a straight line at constant speed.

Newton's first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force.By applying Newton's First Law, when  the spaceship attain a speed of 104 m/s . Then, spaceship will have an uniform motion in a straight line.

Hence, the spaceship will travel in a straight line at constant speed.

Learn more:

https://brainly.com/question/11253532

For each statement about the nuclear force select True or False. In nuclei, it is stronger than the Coulomb force. It acts between a proton and an electron. Its strength goes as 1/distance2, like gravity. It acts between a proton and a neutron. It acts between an electron and a neutron. It acts between two neutrons and also between two protons.

Answers

Answer:

a) True. The Strong interaction is the strong Coulomb force

e) True. It acts between protons, neutrons and between a proton and a neutron

Explanation:

In this exercise you must answer if there are some statements about the nuclei, let's write some of their characteristics

* at the core there is an attractive force called Strong Interaction

* This interaction acts on protons and neutrons alike

* There is a Coulombian-type repulsive force that acts between protons.

Let's review the claims

a) True. The Strong interaction is the strong Coulomb force

b) False. It acts on the elements of the nucleus and here there are no electrons

c) False. It is much greater than gravity and generally described by an exponential

d) False. It acts between components of the nucleus and here there are no electrons

e) True. It acts between protons, neutrons and between a proton and a neutron

A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 16.5 m long. The bowler hears the sound of the ball hitting the pins 2.80 s after the ball is released from his hands. What is the speed of the ball, assuming the speed of sound is 340 m????s?

Answers

Answer:

[tex]5.997m/s[/tex]

Explanation:

We were told to calculate the speed of the ball,

Given speed of sound as 340 m

And we know that the sound of the ball hitting the pins is at 2.80 s after the ball is released from his hands.

Speed of ball = distance traveled/(time of hearing - time the sound travels).

Speed= S/t

Where S= distance traveled

t= time of hearing - time the sound travels

time=time for ball to roll+timefor sound to come back.

time of sound=16.5/340

=0.048529secs

solving for speedof ball

Then,Speed of ball = distance traveled/(time of hearing - time the sound travels).

=16.5/(2.80-0.048529) m/s = 5.997m/s

Therefore, the speed of the ball is

5.997m/s

An air track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0 seconds. It then oscillates with a period of 2.40s and a maximum speed of 30.0 cm/s. What is the glider's position at t=0.300s?

Answers

Answer:

The glider's position at t=0.300s is 8.1 cm

Explanation:

Given;

maximum speed of the glider, [tex]v_{max}[/tex] = 30.0 cm/s = 0.3 m/s

period of the oscillation, T = 2.4 s

Maximum speed of oscillation is given by;

[tex]v_{max}[/tex]  = ωA

Where;

A is the amplitude of the oscillation

ω is the angular speed

[tex]\omega = \frac{2\pi}{T} \\\\\omega =\frac{2\pi}{2.4}\\\\ \omega = 0.833 \pi[/tex]

The amplitude of the oscillation is given by;

[tex]A = \frac{v_{max}}{\omega} \\\\ A = \frac{0.3}{0.833\pi}\\\\ A = 0.1146 \ m[/tex]

The position of the particle is given by;

x(t) = A cosωt

x(0.3) = (0.1146)cos(0.833π x 0.3)

x(0.3) = (0.1146)cos(0.833π x 0.3)

x(0.3) = (0.1146)cos(45)

x(0.3) = 0.081 m

x(0.3) = 8.1 cm

Therefore, the glider's position at t=0.300s is 8.1 cm

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